Horário: 14:00 – 14:40

Speaker : Hermano Frid – Instituto de Matemática Pura e  Aplicada (IMPA-Brasil)  

Title: Short wave-long wave interactions for conservation laws in the relativistic context. 

 Abstract:  In this talk we introduce a framework for modeling the short wave-long wave interactions in the relativistic context. In this context the nonlinear Schr\”odinger equation is no longer suitable for describing short waves and is replaced by a Klein-Gordon equation. Two specific examples are considered: the case where the long waves are governed by a relativistic Burgers equation; and the case where the long waves are governed by the augmented Born-Infeld equations in electromagnetism.   This is a joint work with João Paulo Dias.

 Horário: 14:50 – 15:30

Speaker : Valéria Cavalcanti – Universidade Estadual de Maringá (UEM-Brasil)  

Title: Global existence and asymptotic behaviour of weak solutions for the viscoelastic wave equation with supercritical source

Abstract: The modern viscoelasticity has its origin in the works of Boltzmann and Volterra, who made a connection between the notion of memory with elastic materials.  In this talk we are concerned with the uniform decay of the energy as well as the blow-up of weak solutions for the viscoelastic wave equation with localized memory with past history and supercritical source terms.  This is a joint work with M. M. Cavalcanti, T. D. Marchiori and C. M. Weber.


Horário: 14:00 – 14:40

Speaker : Ma To Fu, Department of Mathematics, University of Brasília, Brasil. 

Title:  Attractors for a semilinear elasticity system featuring damping-vs-delay

 Abstract: In this talk we discuss the long-time dynamics of weakly dissipative elasticity systems with delay effects on the velocity. This damping-vs-delay feature was firstly considered by Nicaise and Pignott (2006) in the context of interior and boundary controllability for wave equations. Our objective is to establish the existence of a smooth finite dimensional global attractor, allowing nonlinearities of critical growth. The main difficulty is finding necessary arguments to show that the system is quasi-stable in the sense of Chueshov and Lasiecka.
[1] S. Nicaise and C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM J. Control Optim. 45 (2006) 1561-1585.
[2] I. Chueshov and I. Lasiecka, Von Karman Evolution Equations. Well-Posedness and Long-Time Dynamics, Springer Monographs in Mathematics, Springer, New York, 2010.
[3] T. F. Ma, J. G. Mesquita and P. N. Seminario-Huertas, Smooth dynamics of weakly damped Lamé systems with delay, SIAM J. Math. Anal. (to appear).

 Horário: 14:50 – 15:30

Speaker : Fernanda Cipriano Department of Mathematics, Universidade NOVA de Lisboa, Portugal

Title: Optimal portfolio for the α-Hypergeometric stochastic volatility model

Abstract: In this talk we study an optimal portfolio problem for an investor with constant relative risk aversion that trades in a market with asset prices described by the α-Hypergeometric stochastic volatility model introduced by Fonseca and Martini.To determine the optimal strategy, we follow the dynamic programming approach. Namely, using a suitable Feynman-Kac representation, we construct a classical solution for the corresponding Hamilton-Jacobi-Bellman equation.  In order to verify that the solution of the Hamilton-Jacobi-Bellman equation coincides with value function, we   establish a verification theorem.

 In addition, we present numerical simulations for the approximation of the value function using a method based on the proposed Feynman-Kac representation.This is a joint work with Nuno Martins and Diogo Pereira.


Horário: 14:00 – 14:40

Speaker : Nicolas Burq ,  Université Paris-Sud, France

Title: Decay rates for Kelvin Voigt damped wave equations

 Abstract: In this talk I will present some recent results about the decay of wave equations with visco-elastic dampings. I will in particular highlight the convergences and differences between this kind of damping and the more classical ones, in terms of — Propagation of singularities — Overdamping phenomena “too much damping kills the damping” — Boundary value problems analysis This is based on joint works with Chenmin Sun (University of Cergy-Pontoise)

 Horário: 14:50 – 15:30

Speaker :  Maria Soledad Aronna , Escola de Matemática Aplicada (FGV EMAp), Brasil

Title: Modeling and analysis of Sterile Insect Technique (SIT) implementation strategies for vector and pest control

Abstract: Joint work with Yves Dumont (CIRAD, Reunion Island, France; and AMAP, University of Montpellier, CIRAD, France; and Department of Mathematics and Applied Mathematics, University of Pretoria,Pretoria, South Africa).
The Sterile Insect Technique (SIT) is a biological control method that consists of releasing males that have been sterilized using ionizing radiation. In the wild, these males mate with wild females that will not produce viable offsprings.
In this talk we present a minimalist model for SIT, assuming that residual fertility can occur in the sterile male population after radiation. Taking into account that we are able to get regular measurements from the biological system along the control duration, such as the size of the wild insect population, we investigate different release strategies that involve either continuous or periodic impulsive releases, in open- and closed-loop forms. We show that a combination of open-loop control with constant large releases and closed-loop nonlinear control leads to the best strategy in terms of both number of releases and total quantity of sterile males to be released. Additionally, we show that SIT fails if the residual fertility is greater than a threshold value that depends on the wild population biological parameters. Moreover, even for small values, the residual fertility induces the use of such large releases, that SIT alone is not always reasonable from a practical point of view.
We provide applications against the mosquito species Aedes albopictus and the fruit fly Bactrocera dorsalis.


Horário: 14:00 – 14:40

Speaker : Jean Pierre Puel , Université de Versailles Saint-Quentin France

Title: Localisation of energy and localised controllability

 Abstract: We consider the wave equation or the Schr\ödinger equation on a domain \Omega. We can define the localised energy on a subdomain D and the starting point of this work was to find an action (control) on the equation in order to obtain a prescribed value of this localised energy. It turns out that this question is equivalent to a localised controllability problem (in the subdomain D). We shall give answers to these questions under some conditions and also some open problems.

 Horário: 14:50 – 15:30

Speaker : Amaury Alvarez Cruz , Instituto de Computação UFRJ – Brazil

Title: Transformation to structured perturbations usingexplicit recurrent procedure for a given family of matrix pencils

Abstract: Matrix polynomials arise in several applications in optimal control, engineering and linear systems theory. One of the practical uses is as approximations of highly nonlinear eigenvalue problems. In this work, we find verssal deformation of Fiedler linearization of the perturbation of matrix coefficients of a polynomial. We focus on the first companion form but the method presented here is possible to extend to a broader class of linearizations. We applied the explicit recurrent procedure to construct a smooth deformation. This construction serves to characterize the perturbation of matrix polynomials and its linearization. Other applications studying the resonance phenomena in the system  of conservation laws are presented.


Horário: 14:00 – 14:40

Speaker : Manuel Milla Miranda , Universidade estadual de paraiba UEPB-Brasil  

Title: Longitudinal Vibrations of a Bar

 Abstract: This conference is concerned with the results on the equation of the small longitudinal vibration of a bar whose one end is clamped and  the other end is glued to a concentrated mass.

 Horário: 14:50 – 15:30

Speaker :  Saulo Pomponet Oliveira , Universidade Federal Do Parana UFPR-Brasil

Title: Métodos aerogeofísicos

Abstract: A interação entre computação científica e geofísica de exploração ocorre predominantemente nos métodos sísmicos, que trazem desafios notáveis na solução de problemas diretos e inversos de propagação de ondas. Talvez
menos conhecidos fora dos departamentos de geologia e de geofísica, métodos aerogeofísicos como a aeromagnetometria e a aerogamaespectrometria também fomentam a pesquisa em técnicas numéricas. O estudo destes métodos é interessante pela disponibilidade de dados obtidos pelo Serviço Geológico do Brasil (CPRM) em levantamentos aéreos que cobrem vasta área do território nacional. Esta apresentação traz um panorama da matemática computacional envolvida, que inclui métodos iterativos de inversão como na sísmica, porém há uma demanda maior por técnicas voltadas para problemas estacionários em vez de transientes.


Horário: 14:00 – 14:40

Speaker :  Harald Helfgott , Universität Göttingen- Alemanha y CNRS-Francia

Title: Los grafos expansores y el problema de paridad.

 Abstract: La noción de grafo expansor puede definirse de varias maneras equivalentes: en términos de las fronteras de conjuntos de vértices, o de valores propios del Laplaciano, o de caminatas aleatorias… Los grafos expansores se han convertido en un objeto central de estudio en las matemáticas discretas; aparte de sus variadas aplicaciones en el estudio de algoritmos, aparecen en la teoría de grupos, la combinatoria y también en la teoría de números. Aparte de dar una introducción a los grafos expansores, hablaré de un resultado reciente mío (todavía por aparecer!) conjunto con M. Radziwiłł. Probamos que unos grafos que codifican cuáles primos en un rango dividen a cada entero son grafos expansores, en un sentido por cierto fuerte. En tanto que corolarios (y usando también un resultado de Matomäki-Radziwiłł-Tao), obtenemos que

lo cual mejora el resultado de Tao sobre la conjectura de Chowla logarítmica en grado 2. Obtenemos también una mejora sobre el trabajo de Tao-Teräväinen sobre la conjectura de Chowla a casi toda escala.

 Horário: 14:50 – 15:30

Speaker :  Edgard Pimentel , Pontifícia Universidade Católica do Rio de Janeiro -Brasil

Title: Fully nonlinear free transmission problems

Abstract: We consider a discontinuous fully nonlinear elliptic operator whose discontinuities depend on the solutions. Such dependence frames the model in the context of free boundary problems. We discuss the optimal regularity of strong  solutions and study the free boundary. In addition, under fairly natural conditions, we prove the existence of $L^p$-viscosity solutions and the existence of strong solutions to the Dirichlet problem associated with our model. This is based on joint works with Makson Santos (CIMAT, Mexico) and Andrzej Święch.


Horário: 14:00 – 14:40

Speaker :  Irena Lasiecka – University of Memphis Department of Mathematical Sciences-United States of America

Title: JMGT [Jordan-Moore Gibson-Thompson] dynamics arising in nonlinear acoustics – a view from the boundary.

 Abstract: A third-order (in time) JMGT equation is a nonlinear (quasilinear) Partial Differential Equation (PDE) model introduced to describe a nonlinear propagation of high frequency acoustic waves. The interest in studying this type of problems is motivated by a large array of applications arising in engineering and medical sciences-including high intensity focused ultrasound [HIFU] technologies, lithotripsy, welding and others. The important feature is that the model avoids the infinite speed of propagation paradox associated with a classical second order in time equation referred to as Westervelt equation. Replacing a classical heat transfer by heat waves gives rise to the third order in time derivative scaled by a small parameter τ > 0, the latter represents the thermal relaxation time parameter and is intrinsic to the properties of the
medium where the dynamics occurs.
The aim of the present lecture is to provide a brief overview of recent results in the area which are pertinent to both linear and non-linear dynamics. From the mathematical point of view JMGT, can be seen as a nonlinear perturbation of a third order strictly hyperbolic system, which however has a characteristic boundary. This feature has, of course, strong implications on boundary behavior [both regularity and controllability] which can not be patterned after classical hyperbolic systems theory [as it is the case for the wave equation]. As a consequence, the analysis of regularity [both forward and inverse estimates] is
particularly challenging-even in the linear case. Several recent results pertaining to boundary stabilization, with Neumann non-dissipative boundary and related optimal control with boundary actuation and infinite horizon will be presented
and discussed. In all these case, peculiar features associated with the third order dynamics leads to novel phenomenological behaviors. The work presented is in collaboration with Marcelo Bongarti and Jose Rodriguez.

 Horário: 14:50 – 15:30

Speaker : Jaqueline Godoy Mesquita – Universidade de Brasília, UnB – Brasil

Title: Linearized instability for neutral functional differential  equations with state-dependent delays. 

Abstract: In this talk, we will give a brief overview of a class of equations called _neutral functional differential equations with state-dependent delays_, describing some important applications. After this, we will show some recents results in the area, and we will present a principle of linearized instability for these equations.This is a joint work with Professor Bernhard Lani-Wayda


Horário: 14:00 – 14:40

Speaker :  Marcelo Moreira Cavalcanti – Universidade Estadual de Maringá – Brasil

Title: Exponential decay for the semilinear wave equation with localized frictional and Kelvin-Voigt dissipating mechanisms 

Abstract: In the present talk, we are concerned with the semilinear viscoelastic wave equation in an inhomogeneous medium $\Omega$ subject to two localized dampings. The first one is of the type viscoelastic and is distributed around a neighborhood $\omega$ of the boundary according to the Geometric Control Condition. The second one is a frictional damping and we consider it hurting the geometric condition of control.  We show that the energy of the wave equationgoes uniformly and exponentially to zero for all initial data of finite energy taken in bounded sets of finite energy phase-space.

 Horário: 14:50 – 15:30

Speaker : Eduardo González – Pontificia Universidad Catolica de Valparaiso-Chile  

Title: Bifurcaciones, periodicidad y multiples estabilidades en modelos de depredacion de tipo Gause. Una breve revision

 Abstract: En esta presentacion expondremos las principales propiedades de un tipo de modelos compartimentados de depredacion tiempo continuo, denominados modelos de tipo Gause [2]. Es bien sabido que las interacciones depredador-presa dependen fuertemente tanto de las tasas de crecimiento de la poblacion de presas y depredadores, como
de la acciÛn de depredaciÛn denominada la respuesta funcional [7]. Esta funcion la consideraremos solo dependiente de la poblacion de presas (respuesta funcional presa-dependiente) [6], usando principalmente las formas matematicas mas usuales [3], clasificadas como tipos Holling I, II, III y IV [4]. El objetivo principal será establecer condiciones para la existencia o no de ciclos lÌmites (soluciones periodicas) [1] y algunas de las bifurcaciones mas conocidas en sistemas planares tiempo continuo [5].

[1] K.S.Cheng, Uniqueness of a limit cycle for a predator-prey system, SIAM Journal on Applied Mathematics 12 (1981) 541-548.[2] G. F. Gause, The struggle for existence, The Williams & Wilkins company, 1934. [3] E. Gonz·lez-Olivares and A. Rojas-Palma, Allee e§ect in Gause type predator-prey models: Existence of multiple attractors, limit cycles and separatrix curves. A brief review. Mathematical Modelling of Natural Phenomena 8(6) (2013) 143-164. [4] C. S. Holling, The components of predation as revealed by a study of small-mammal predation of the European pine sawáy, Canadian Entomologist 91(1959) 293-320. [5] Y. A. Kuznetsov, Elements of applied bifurcation theory (2nd Edition), Springer-Verlag (1998). [6] R. M. May, Stability and complexity in model ecosystems (2nd edition), Princeton University Press (2001). [7] P. Turchin, Complex Population Dynamics: A Theoretical/Empirical Synthesis, Princeton University Press, Princeton, New Jersey, 2003.


Horário: 14:00 – 14:40

Speaker : Sérgio Almaraz – Universidade Federal Fluminense -UFF, Brasil

Title: Teoremas de massa positiva e problemas do tipo Yamabe

Abstract: O problema de Yamabe é uma questão de uniformização de variedades Riemannianas que foi proposta em 1960. Essa questão proporcionou enorme desenvolvimento no emprego de técnicas de Equações Diferenciais Parciais em Geometria Diferencial. O passo final na sua resolução, dado por R. Schoen em 1984, apresentou uma relação entre o problema de Yamabe e a teoria da Relatividade Geral de Einstein. Esse passo envolve a prova do teorema da massa positiva para sistemas isolados assintoticamente planos. Nessa palestra, discutirei um pouco os conceitos básicos envolvidos no tema bem como problemas similares e recentes, apresentando um pouco das minhas linhas de pesquisa e resultados relacionados

Horário: 14:50 – 15:30

Speaker : Roxana Lopez CruzIDIC-ULIMA Y UNMSM, Perú

Title: Un modelo epidemiológico SAIRD con retroalimentación negativa

Abstract: Las epidemias por su naturaleza dinámica tienen su modelación matemática básica la cual se va tornando más compleja según como se vaya considerando más factores que caracterizan a cada enfermedad. Sin embargo, hay factores externos a la enfermedad que influencian en la incidencia de esta y ellos son generados por ejemplo por prejuicios sobre campañas de vacunación con previa información (retroalimentación negativa), como el caso del concepto negativo en la población con respecto a la vacuna contra el virus del papiloma humano (VPH), muchas veces causado por desinformación. En este trabajo proponemos y analizamos un modelo epidémico en ecuaciones diferenciales que define la función índice de información y el efecto de la retroalimentación negativa en el parámetro de tratamiento no farmacéutico (por ejemplo: cuarentenas). Los resultados matemáticos y de simulación nos proporcionaran los diversos escenarios de la dinámica de la enfermedad que nos ayudara a mostrar la importancia por ejemplo de una buena información en cuanto a las cuarentenas.


Horário: 14:00 – 14:40

Speaker : Alexandre Madureira, Laboratorio Nacional de Computaçao Cientifica-LNCC-Brasil

Title: Multi-generational SIR modeling: determination of parameters, epidemiological forecasting and age-dependent vaccination policies

Abstract: We use an age-dependent SIR system of equations to model the evolution of the COVID-19. Parameters that measure the amount of interaction in different locations (home, work, school, other) are approximated using a random optimization scheme, and indicate changes in social distancing along the course of the pandemic. That allows the estimation of the time evolution of the  classical and age-dependent reproduction numbers $\R_0$. With those parameters we predict the disease dynamics, and compare our results with data from several locations in Brazil. We also provide a preliminary investigation regarding age-based vaccination policies, indicating connections between the age of those immunized, contagious parameters and vaccination schedules.

Horário: 14:50 – 15:30

Speaker :Mauricio Sepúlveda Cortés, Departamento de Ingenieria Matemática, Universidad de Concepción-Chile

Title: Energy Conservative Finite Difference Methods for Dispersive Equations

Abstract: Some numerical methods are presented for equations that model the propagation of waves or dispersive solitons, such as the Korteveg-de Vries as fluid models, or the high-order Schrödinger equation with applications in wave propagation in optical fibers. In these models the nonlinear terms generate some difficulties both in the analysis and in the numerical approximations. Within the possibilities, a numerical discretization is chosen that conserves the L2 norm or the energy associated with the equation. This helps to make discrete estimates of energy and demonstrate stability. Additionally, the stability and exponential decay of energy is studied by adding different types of damping or memory terms on the equations


Horário: 14:00 – 14:40

Speaker : André Nachbin, Instituto de Matemática Pura e Aplicada-IMPA, Brasil

Title: Integração singular visando um operador de diferenças finitas com precisão espectral

Abstract: É sabido que um operador de diferenças finitas aproxima uma derivada apresentando uma taxa (fixa) de convergência algébrica. No entanto, vamos exibir um novo operador de diferenças finitas e provar que tem precisão espectral. Ou seja, a taxa de convergência não é fixa e melhora de acordo com a regularidade da função. Por exemplo, a convergência é exponencial para funções analíticas. Nossa metodologia não é padrão em Teoria da Aproximação, pois não usa aproximação polinomial nem qualquer outro tipo de base. Nosso método se baseia simplesmente na manipulação numérica de integrais singulares, usando quadraturas precisas para integrais do tipo Valor Principal de Cauchy. O núcleo da integral é uma distribuição, o que dá lugar a um esquema multi-resolução. O respectivo método de diferenças finitas distribucional apresenta “stencils” de todas as resoluções possíveis na grade, estimando derivadas de uma forma não-local. Apresentaremos ilustrações computacionais deste novo método e faremos comparações com outro método recente (não-convencional) de diferenças finitas, que faz uso de um passo complexo para lidar melhor com o erro de arredondamento.

Horário: 14:50 – 15:30

Speaker :Eduardo Cerpa, Instituto de Ingeniería Matemática y Computacional- Pontificia Universidad Católica de Chile, Chile

Title: Effect of time scales on stability of coupled systems involving the wave equation

Abstract: This talk considers systems coupling an ordinary differential equation (ODE) with a wave equation through its  boundary data. The main focus is put on the role of different time scales for each equation on the stability of the coupled system. In this context it is natural to apply the singular perturbation method but for infinite-dimensional systems it is known that in some cases this method does not work. Indeed, you can not be sure of the stability of the full system even if the given subsystems are stable. This is the case when coupling a wave equation to a fast ODE. On the other hand, when coupling a fast wave equation with an ODE, the system is proven to be stable if each subsystem is stable. We use the singular perturbation method to get that result and a Tikhonov theorem, which is the first of this kind for systems involving the wave equation.


Horário: 14:00 – 14:40

Speaker : Octavio Paulo Vera Villagran

Title: Exact Solution For a Benney-Lin Equation Type

Abstract: An exponential traveling-wave solution of the free surface equation for a viscous film flowing down an inclined plane is presented. We use the Ince transformation.

Horário: 14:50 – 15:30

Speaker : Teófilo Domingos Chihaluca, Universidade da Beira Interior

Title: Aproximação Numérica de Equações Diferenciais Parciais Não Lineares com Aplicação em Finanças

Abstract: É feita a regularização da equação Delta de Black-Scholes não linear para o modelo de custo de transação. Prova-se a existência de solução clássica da equação regularizada e prova-se que esta converge para a solução viscosa do problema. Demonstra-se que a ordem convergência da solução semi-discreta e a da totalmente discreta. Para o cálculo de opções americanas, acrescentou-se um termo de penalidade no segundo membro e a condição da derivada para localizar a fronteira. No final, o método é implementado em ambiente Matlab e são apresentados alguns resultados numéricos.


Horário: 14:00 – 14:40

Speaker : Diogo Gomes , King Abdullah University of Science and Technology-Saudi Arabia

Title: Algorithms for PDEs

Abstract: The qualitative study of PDEs often relies on integral identities and inequalities. For example, for time-dependent PDEs, conserved integral quantities or quantities that are dissipated play an important role. In particular, if these integral quantities have a definite sign, they are of great interestas they may provide control on the solutions to establish well-posedness. Finding these integral identities and inequalities is a tedious task that relies on a combination of heuristics and skill. However, as we will see in this talk, finding conserved and dissipated quantities for PDEs is an algorithmic task that can be automated. We will discuss some ongoing progress in this area,the key tools used (exact linear algebra, calculus of variations and quantifier elimination methods) and present some applications to the theory of mean-field games. We will also address semi-discretization of partial differential equations and how our methods can be used in these problems.

Horário:14:50 – 15:30

Speaker : Sandra Malta , Laboratório Nacional De Computação Cientifica-Brazil

Title: Um modelo SEIRD generalizado para a COVID-19 com mecanismo implícito de distanciamento social.

Abstract: Desenvolvemos um modelo SEIRD generalizado onde são consideradas  medidas de distanciamento social, com o objetivo de deter a disseminação da COVID-19. Para a identificação dos parâmetros dos modelos e a quantificação das incertezas é aplicada uma análise bayesiana. Diferentes estratégias de relaxamento das medidas de distanciamento social são investigadas, buscando aquelas que produzem maior impacto no achatamento da curva de infectados. São apresentados resultados para o Brasil e o estado do Rio de Janeiro.


Horário: 14:00 – 14:40

Speaker : Luz de Teresa, Universidade Federal de Paraíba/ Universidad Nacional Autónoma de México

Title: Algunos resultados de diseño de observadores para EDP

Abstract: El problema del diseño de observadores surge de la necesidad de monitorear sistemas de control en tiempo real. Es
decir, se busca estimar, de la mejor manera, las variables de estado del sistema, a partir de la informaci on (limitada) medible obtenida del sistema. Dicha informaci on es obtenida mediante sensores colocados en regiones accesibles del sistema, ya sea en el interior o en la frontera del dominio del sistema. El diseño de observadores tiene diversas aplicaciones, por ejemplo en detecci on de fallas, estimaci on de par ametros, reconstrucci on de modelos. En esta charla presentaremos algunos resultados para la ecuación del calor semilineal y presentaremos algunos avances para la ecuación de ondas.

Horário:14:50 – 15:30

Speaker : Antônio Leitão, Universidade Federal de Santa Catarina , Brazil

Title: Uma tarde com problemas inversos e mal-postos

Abstract: Nesta palestra será apresentada, por meio de exemplos, uma área de pesquisa da matemática aplicada, a saber “problemas inversos”. Algumas questões desafiadoras relacionadas aos problemas matemáticos dessa área serão o discutidas. A tarefa de como obter soluções (de forma estável) para problemas mal-postos será investigada.


Horário: 14:00-14:40

Speaker: Felipe Linares, Instituto de Matemática Pura e Aplicada (IMPA) Brazil

Title: On long time behavior of solutions of the Schrödinger-Korteweg-de Vries system

Abstract: In this lecture we will be concerned with the decay of long time solutions of the initial value problem associated with the Schrödinger-Korteweg-de Vries system. We use recent techniques in order to show that solutions of this system decay to zero in the energy space. Our result is independent of the integrability of the equations involved and it does not require any size assumptions.

Horário: 14:50-15:30

Speaker: Paulo Amorim, Instituto de Matemática da  Universidade Federal de Rio de Janeiro (IM-UFRJ) Brazil

Title: A model of self-propelled agents interacting through pheromone: individual and collective behavior 

Abstract: We present a model of self-propelled agents navigating on a landscape oriented by a pheromone signal. The model is heavily motivated by ant navigation. We begin by deducing the model from biological considerations, where each individual orients itself according to the presence of the pheromone in a small circular sector around it. We present some stability properties of trail-like solutions when the trail is given, showing that trail-following behavior is a stable feature of the model. Next, we show the model’s consistency with some experimental results. We proceed to the analysis of the model in the case where the pheromone field is produced by a large number of interacting agents. This gives rise to a system of $N$  ODEs coupled by a diffusion equation, which we analyze. Finally, we provide some numerics to illustrate the collective, self-organizing behavior.


Horário: 14:00-14:40

Palestrante: Marko Rojas-MedarUniversidad de TarapacáArica, Chile

Titulo: Formalismo de Duvobitski-Milyutin e suas aplicações em EDP

Resumo: Apresentamos uma revisão da teoria desenvolvida por Dubovitskii e Milyutin sobre as condições de otimalidade para problemas de otimização com um ou múltiplos objetivos. Os resultados de Dubovitskii e Milyutin permitem obter condições de otimalidade para problemas de otimização em espaços localmente convexos e podem ser aplicados em diferentes áreas. Em particular, mostraremos sua aplicação na caracterização do ótimo no sentido de Pareto e Nash quando a dinâmica do sistema é governada pelas equações de Navier-Stokes.

Horário: 14:50-15:30

Speaker: Sônia M. Gomes – IMECC-Unicamp  Brazil

 Title: Two-scale Hybrid-Mixed Methods for Linear Elasticity with Weak Stress Symmetry

 Abstract: We present a multiscale hybrid-mixed method for linear elasticity problems on general polytope meshes. The new methods approximate displacement, stress, and rotation using two-scale discretizations. The first scale level setting consists of approximating the traction variable (Lagrange multiplier) in discontinuous polynomial spaces, and of computing rigid body modes element wisely. In the second level, the methods are made effective by solving completely independent local boundary Neumann elasticity problems written in a mixed form with weak symmetry enforced via a rotation multiplier. Since the finite-dimensional space for the traction variable constraints the local stress approximations, the discrete stress field lies in the H(div) space globally and stays in local equilibrium with external forces. We propose different choices to approximate local problems based on pairs of finite element spaces defined on affine second-level meshes. Those choices generate the family of multiscale finite element methods for which stability and convergence are proved in a unified framework. Notably, we prove that the methods are optimal and highorder convergent in the natural norms. Also, it emerges that the approximate displacement and stress divergence are super-convergent in the L2-norm. Numerical verifications assess theoretical results and highlight the high precision of the new methods on coarse meshes for multilayered heterogeneous material problems. Joint work with: P. R. Devloo, A. M. Farias, A. B. dos Santos, W. Pereira and F. Valentin  


Horário: 14:00-14:40

Speaker: Boyan Sirakov , Departamento de MatemáticaPUC – Rio, Brasil


Abstract: We prove that the Dirichlet problem for the Lane-Emden equation in a halfspac has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is bounded on finite strips. This question has a long history and our result solves a long-standing open problem. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. The result extends to general convex nonlinearities.

Horário: 14:50-15:30

Speaker: Francisco Manuel Guillen Gonzalez, Dpto. de Ecuaciones Diferenciales y Análisis Numérico Universidad Sevilla, Spain 

Title: Some bilinear optimal control problems related to chemotaxis PDE models

Abstract: In this talk we show some recent results for bilinear optimal control subject to several chemo-repulsion and production models (changing the production function). Three type of results will be presented; existence of global optimal solution, a necessary optimality system based on the existence of Lagrange multipliers, and a posteriori regularity result for these Lagrange multipliers.


Horário: 14:00-14:40

Speaker: Jorge P Zubelli , Khalifa University, Abu Dhabi, UAE , IMPA, Rio de Janeiro, Brazil 

Title: A Splitting Strategy for the Calibration of Jump-Diffusion Models

Abstrac: This talk concerns the calibration of Dupire’s model in the presence of jumps. This leads to an integro-differential equation whose parameters have to be calibrated so as to fit market data. We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time and price dependent volatility.
Our approach uses a forward Dupire-type partial-integro-differential equation for the option prices to produce a parameter-to-solution map. The ill-posed inverse problem for such a map is then solved by means of a Tikhonov-type convex regularization. We present numerical examples that substantiate the robustness of the method  both for synthetic and real data. This is joint work with Vinicius Albani (UFSC) that just appeared in Finance and Stochastics.

Horário: 14:50-15:30

Palestrante: Maicon R. Correa , Instituto de Matemática, Estatística e Computação Científica, Unicamp – Brazil

Titulo: Numerical Schemes for Multiphase Flow in Poroelastic Media

Resumo: In this talk, we present a sequential iterative algorithm for numerically solving the coupled nonlinear system of partial differential equations that models multiphase-flow in highly heterogenous poroelastic media, and discuss the use of different mixed Finite Element Methods for the (linearized) elliptic subproblems of flow and geomechanics. In particular, we focus on the use of accurate and stable mixed-hybrid finite element methods to compute Darcy’s velocity and pressure in highly heterogeneous porous media and the pair stress-displacement in linearly elastic isotropic media.


Horário: 14:00 – 14:40

Conferencista: Enrique Zuazua

Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

Deusto Foundation, Bilbao, Spain

Universidad Autónoma de Madrid, Spain

Título: Control Turnpike y Aprendizaje Profundo 

Resumo: El principio de Turnpike afirma que en grandes horizontes temporales las estrategias de control óptimas son casi de naturaleza  estacionaria. En esta conferencia estudiaremos algunos resultados recientes sobre este tema y presentaremos algunas de sus consecuencias en el aprendizaje supervisado profundo. La charla se basará en particular en el reciente trabajo conjunto con C. Esteve, B. Geshkovski y D. Pighin.

Horário: 14:50 – 15:30

Palestrante: Daniel G. Alfaro Vigo (Departamento de CIência da Computação – UFRJ)

Título: Um método aproximado para a equação de Korteweg-de Vries com dissipação  

Resumo: A equação de Korteweg-de Vries (KdV) representa um modelo matemático simplificado da propagação, em um meio dispersivo, de ondas unidirecionais não lineares e de pequena amplitude. Nos últimos anos a equação KdV com dissipação tem despertado muito interesse na comunidade matemática.  Nesta palestra, vamos apresentar resultados sobre a existência e unicidade de soluções, e a influência do mecanismo de dissipação na energia do sistema para a equação KdV com dissipação em um domínio limitado. Será abordado um método numérico baseado na discretização por elementos finitos no espaço e pelo esquema de diferenças finitas de Crank-Nicolson no tempo. Será apresentada a análise numérica desse método aproximado e também discutiremos os resultados de simulações numéricas. Este trabalho foi realizado em colaboração com Mauro A. Rincon (UFRJ) e Juliana C. Xavier (UTFPR).


Horário: 14:00 – 14:40

Speaker: E. Fernández-Cara, Universidad de Sevilla (Spain)

Title: Controlling fluids: motivations and some recent results

Abstract: The Navier-Stokes equations have been studied since many years. They are very relevant in mathematics and physics and many people have been concerned with the solution of several related major open problems. On the other hand, the control of PDEs has attracted a lot of work the last decades. This has been motivated by its relevant role in applications. This talk is devoted to present some recent results dealing with the control of systems of the Navier-Stokes kind. We will consider some (new) optimal control and controllability problems and we will discuss theoretical and numerical aspects.

Horário: 14:50 – 15:30

Palestrante: Nuno Crokidakis, Instituto de Física, Universidade Federal Fluminense (Brasil)

Título: Analisando o potencial para uma segunda onda de casos na evolução da COVID-19 em economias emergentes e em desenvolvimento

Resumo: O distanciamento social, alcançado pela restrição da mobilidade humana, é apontado como a estratégia mais eficiente contra a evolução da COVID-19. No entanto, pressões econômicas dificultam a implementação dessa medida. Em primeiro lugar, os indivíduos que dependem dos rendimentos da economia informal são mais afetados por tais restrições e, consequentemente, menos propensos a respeitar as políticas de restrição à mobilidade. Em segundo lugar, se as restrições forem suspensas logo após os níveis de infecção atingirem um pico e começarem a diminuir continuamente, uma segunda onda de infecções pode surgir e aumentar o custo da pandemia. Analisamos o impacto desses dois fatores na evolução da pandemia de COVID-19 através de um modelo de duas populações Suscetível-Infectado-Recuperado-Assintomático-Sintomático-Morto (SIRASD), onde os indivíduos diferem apenas pelo seu grau de conformidade com políticas de distanciamento social. Embora nossa abordagem seja válida para qualquer país emergente, onde o número de pessoas envolvidas na economia informal representa uma grande parcela da força de trabalho total e, portanto, propenso a não seguir o auto-isolamento, usamos dados do Brasil, um país que apresenta estas características, a fim de fornecer resultados numéricos convincentes. Com base em parâmetros derivados de dados de propagação da COVID-19 no Brasil, concluímos que se as medidas de confinamento forem suspensas muito cedo, ou seja, até uma semana de diminuição consecutiva do número de novos casos, é muito provável que o aparecimento de um segundo pico.


14:00 – 14:40

Speaker: Roberto Guglielmi, Department of Applied Mathematics, University of Waterloo, Canadá

Title: Bilinear Optimal Control of the Fokker-Planck Equation

Abstract: For a large class of stochastic processes, the evolution of the probability density function associated to the process is ruled by the Fokker-Planck equation. Following a statistical approach, we recast an optimal control problem subject to a stochastic differential equation in terms of an optimal control problem for the Fokker-Planck equation. Motivated by this relation, in this talk we study the optimal control problem of the Fokker-Planck equation through a bilinear control acting as the coefficient of the divergence in the advection term. We extend previous results to the case of a control which depends on time and space. We give suitable conditions to ensure the existence of nonnegative solutions for the state equation, the existence of optimal controls, and we develop the associated first order necessary optimality conditions. Finally, numerical simulations show the effectiveness of the proposed control strategy.

14:50 – 15:30

Palestrante: Marcelo Goulart Teixeira, Departamento de Ciências da Computação, Universidade Federal do Rio de Janeiro, Brasil

Título: Um novo modelo constitutivo para a cortiça

Resumo: A cortiça é um material natural utilizado pelo homem há mais de 5000 anos, normalmente em aplicações de natureza doméstica. Seu uso mais comum, como rolha para garrafas de vinho, data do início do século XVII e deve-se ao monge beneditino Dom Perignon. Porém, nos últimos anos, devido a características tais como baixa densidade, boa elasticidade, boa recuperação a ações compressivas e uma quase total impermeabilidade, além de excelente isolamento térmico, acústico e vibrático, a cortiça tem sido usada em um vasto campo de aplicações, nomeadamente em construção civil, nas indústrias naval e aeroespacial e na manufatura de equipamentos de segurança. Considerada um material hiperelástico, a cortiça é o único sólido que não sofre dilatação lateral. Dessa forma, a simulação numérica de problemas de grande deformação envolvendo a cortiça possui dificuldades interessantes do ponto de vista numérico. Nesta palestra vamos mostrar algumas propriedades mecânicas da cortiça, discutir as dificuldades de sua modelagem e apresentar um novo modelo constitutivo para este material. Será abordado também o método ALI (Aproximação Linear Incremental), um método Lagrangeano-Euleriano atualizado linearizado, e sua utilização na simulação de dois problemas clássicos de grande deformação envolvendo a cortiça.