Seminar october 18 of 2023

Seminar october 18 of 2023

por | out 13, 2023 | Sem categoria

Seminar in EDP and Applied Mathematics

October 18, 2023 – 14h (Brazil)

Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA 

Youtube Channel

Event

About Seminars

Our Online Seminar is one of the most important events in Brazil, it has been held since August 2020, every Wednesday at 2 pm, Brasília time, with a frequency of 14 days. Two 40-minute lectures are presented in each session. Our speakers are world-renowned mathematicians from Europe, the United States and South America.

Featured Talks & Speakers

Claudio Muñoz

CNRS and Universidad de Chile,France-Chile

14:00h – 14:40h

On the soliton dynamics in Boussinesq systems

 In this talk, I will review recent results in collaboration with several authors on the soliton dynamics in Boussinesq systems, including abcd, improved, good, and the fourth-order phi 4 model. The idea is to show and explain how long time behavior is obtained by using well-defined virial identities.

Alex Himonas

Department of Mathematics University of Notre Dame-United States

14:50h – 15:30h

Initial-boundary value problems for evolution equations and systems via the Fokas method

The Fokas unified transform method  (UTM) provides a novel approach for solving initial-boundary value problems (ibvp’s) for linear and integrable nonlinear partial differential equations.  In particular, it gives solution formulas for forced linear ibvp’s. Using these formulas Fokas and collaborators initiated a new approach for studying  the well-posedness in Sobolev spaces of ibvp’s for nonlinear evolution equations, which is analogous to the way well-posedness of initial value problems (ivp’s) are studied based on the Fourier method. Utilizing the Fokas solution formulas linear estimates are derived and then
using the multilinear estimates suggested by the nonlinearity it is shown that the iteration map defined by this formula is a contraction in appropriate solution spaces. In this talk we will present key points of this approach for the Korteweg-de Vries, the nonlinear Schr\”odinger and related equations and systems.
The talk is based on collaborative work with A. Fokas, D. Mantzavinos and F. Yan. 

About Organization

Juan Limaco – UFF – Brazil (Coordenador);
Mauro Rincon – UFRJ – Brazil
Max Souza – UFF – Brazil;
Sandra Malta – LNCC – Brazil
Marcelo Cavalcanti – UEM – Brazil;
Rui Almeida – UBI – Portugal
Roxana Lopez – UNMSM – Peru;
Diego Souza – U Sevilla – España;
Mauricio Sepulveda – UdeC – Chile;
Roberto Capistrano – UFPE – Brazil.

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Seminar october 4 of 2023

Seminar october 4 of 2023

por | set 30, 2023 | Sem categoria

Seminar in EDP and Applied Mathematics

october 4 , 2023 – 14h (Brazil)

Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA 

Youtube Channel

Event

About Seminars

Our Online Seminar is one of the most important events in Brazil, it has been held since August 2020, every Wednesday at 2 pm, Brasília time, with a frequency of 14 days. Two 40-minute lectures are presented in each session. Our speakers are world-renowned mathematicians from Europe, the United States and South America.

Featured Talks & Speakers

Patrick Gerard

Laboratoire de Mathématique d’Orsay, CNRS & Université Paris-Saclay-France

14:00h – 14:40h

The zero dispersion limit for the Benjamin-Ono equation on the line

The Benjamin-Ono equation was introduced in 1967 in order to describe long internal gravity waves in a two-layer fluid with an infinite depth. It is a nonlinear dispersive Hamiltonian PDE enjoying integrability properties. In this talk, I will explain how these integrability properties allow us to identify the zero dispersion limit of any solution with a bounded and square integrable datum on the line. The result will be described in terms of Brenier’s transport-collapse scheme for the inviscid Burgers equation.

Jesus Ildefonso  Diaz

Universidad Complutense de Madrid, Spain

4:50h – 15:30h

Beyond the classical strong maximum principle:forcing changing sign near the boundary and flat solutions

 

In a pioneering paper, on 1910, S. Zaremba established the \textit{strong maximum principle} saying that if $\Omega$ is a smooth bounded domain in $% \mathbb{R}^{N}$ and a function $u$ verifies \begin{equation}\left\{\begin{array}{lr} -\Delta u\geq f(x) & \text{in }\Omega , \\u=0 & \text{on }\partial \Omega ,%\end{array}%\right. \label{ProbLineal}\end{equation}% \noindent then \begin{equation} u(x)>0\text{ in }\Omega , \tag{P$_{u}$} \label{Positiv u} \end{equation} \noindent assumed that \begin{equation} f(x)\geq 0\text{ in }\Omega ,\text{ }f\neq 0. \tag{P$_{f}$} \label{Positiv f} \end{equation} The extension to a more general second order elliptic operator was due to E. Hopf, on 1927. Moreover, some years later, on 1952, E. Hopf and O.A. Oleinik, independently, proved that under the above conditions the normal derivative of $u$ satisfies the following sign condition \begin{equation} \frac{\partial u}{\partial n}<0\text{ on }\partial \Omega . \label{Hypo2.3} \end{equation}. The main goal of this lecture is to show that the non-changing sign assumption (\ref{Positiv f}) can be removed in a suitably way (for instance when $f(x)<0$ in some neighborhood of $\partial \Omega $)$.$ Under such type of new assumptions on $f$ we can prove that: (A) the positivity of $u,$ property (\ref{Positiv u}), still holds and $% \frac{\partial u}{\partial n}\leq 0$ on $\partial \Omega ,$ \noindent and (B) under additional conditions on $f(x)$, the positive \textit{solution} of the equation (\ref{ProbLineal}) [i.e., now with the identity symbol $=,$ instead $\geq $] does not satisfy (\ref{Hypo2.3}) but $\frac{\partial u}{% \partial n}=0$ on $\partial \Omega $ \ (this corresponds to the notion of \textit{flat solutions} already considered by different authors in the framework of some nonlinear problems). The above extension of the strong maximum principle admits many generalizations (nonlinear elliptic operators, zero and first order terms, etc.). In the case of linear parabolic problems%\[ \left\{\begin{array}{lr} u_{t}-\Delta u=f(x,t) & \text{in }\Omega \times (0,+\infty ), \\ u=0 & \text{on }\partial \Omega \times (0,+\infty ), \\ u(x,0)=u_{0}(x) & \text{on }\Omega ,% \end{array}% \right.\]% it can be proved that, under suitably changing sign conditions on $u_{0}(x)$ and/or on $f(x,t)$ (even if it occurs for any $t>0$), we get the global positivity of $u(x,t)$ on $\Omega $, for large values of time ( $\exists $ $% t_{0}\geq 0$ such that $u(x,t)>0$ a.e. $x\in \Omega ,$ for any $t>t_{0}$). An application to some \textit{sublinear} \textit{indefinite} semilinear equations will be also given. [Joint results with Jes\'{u}s Hern\'{a}ndez].

About Organization

Juan Limaco – UFF – Brazil (Coordenador);
Mauro Rincon – UFRJ – Brazil
Max Souza – UFF – Brazil;
Sandra Malta – LNCC – Brazil
Marcelo Cavalcanti – UEM – Brazil;
Rui Almeida – UBI – Portugal
Roxana Lopez – UNMSM – Peru;
Diego Souza – U Sevilla – España;
Mauricio Sepulveda – UdeC – Chile;
Roberto Capistrano – UFPE – Brazil.

Our Partners

Access our channel!

A channel for students, professors, researchers and professionals who wish to deepen their knowledge in EDP and applied mathematics.

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Seminar september 20 of 2023

Seminar september 20 of 2023

por | set 14, 2023 | Sem categoria

Seminar in EDP and Applied Mathematics

september 20, 2023 – 14h (Brazil)

Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA 

Youtube Channel

Event

About Seminars

Our Online Seminar is one of the most important events in Brazil, it has been held since August 2020, every Wednesday at 2 pm, Brasília time, with a frequency of 14 days. Two 40-minute lectures are presented in each session. Our speakers are world-renowned mathematicians from Europe, the United States and South America.

Featured Talks & Speakers

Adrian Constantin

Faculty of Mathematics, University of Vienna, Austria

14:00h – 14:40h

Existence and stability results for stratospheric planetary flows

We will discuss stratospheric planetary flows in the
atmosphere of the outer planets of our solar system, modelled by
stationary solutions of Euler’s equation on a rotating sphere.
We present some rigidity results, ensuring that the solutions are
either zonal or rotated zonal solutions, and discuss the stability
of Rossby–Haurwitz waves.

Cristina Pignotti

Dipartimento di Matematica Pura e Applicata, Universitá di L’Aquila,Italy

14:50h – 15:30h

Decay estimates for semilinear wave equations with time-dependent time delay

We analyze a class of semilinear damped wave-type equations with a delay feedback with time-variable time delay. Under suitable assumptions on the system’s parameters, by combining semigroup arguments, careful energy estimates, and an iterative approach, we are able to prove a well-posedness result and an exponential decay estimate for solutions corresponding to small initial data. An extension to viscoelastic wave equations with time delay is also discussed.

About Organization

Juan Limaco – UFF – Brazil (Coordenador);
Mauro Rincon – UFRJ – Brazil
Max Souza – UFF – Brazil;
Sandra Malta – LNCC – Brazil
Marcelo Cavalcanti – UEM – Brazil;
Rui Almeida – UBI – Portugal
Roxana Lopez – UNMSM – Peru;
Diego Souza – U Sevilla – España;
Mauricio Sepulveda – UdeC – Chile;
Roberto Capistrano – UFPE – Brazil.

Our Partners

Access our channel!

A channel for students, professors, researchers and professionals who wish to deepen their knowledge in EDP and applied mathematics.

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Seminar september 6 of 2023

Seminar september 6 of 2023

por | set 2, 2023 | Sem categoria

Seminar in EDP and Applied Mathematics

september 6, 2023 – 10h (Brazil)

Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA 

Youtube Channel

Event

About Seminars

Our Online Seminar is one of the most important events in Brazil, it has been held since August 2020, every Wednesday at 2 pm, Brasília time, with a frequency of 14 days. Two 40-minute lectures are presented in each session. Our speakers are world-renowned mathematicians from Europe, the United States and South America.

Featured Talks & Speakers

Yihong Du

University of New England –Australia

10:00h – 10:40h

Long-time dynamics of two invading competitors

 In this talk I will discuss the eventual outcomes of two invading competitors based on a two species diffusive competition model with free boundaries. We are interested in a complete understanding of all the possible invading profiles of the system in the weak-strong competition case, where a strong competitor and a weak competitor invade the spatial environment simultaneously. We show that there are exactly five different types of invading profiles for this system. This talk is based on theoretical work with Chang-Hong Wu (Taiwan), and numerical work with K. Khan (Australia), Shuang Liu (USA) and T. Schaerf (Australia). 

Miguel Nuñez

Univ. Federal de Mato Grosso-Brazil 

10:50h – 11:30h

Hierarchical Controllability for a Nonlinear Parabolic Equation in One Dimension.

This work deals with the hierarchical control of a nonlinear parabolic equation in one dimension. The novelty in this work is the appearance of the spatial derivative of the solution instead of considering only the solution in the quasilinear term (nonlinearity), here lies the difficulty of approaching said equation. We use Stackelberg–Nash strategies. As usual, we consider one control called leader and two controls called followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem, then, we look for a leader that solves null and trajectory controllability problems. First, we study the linear problem and then, we use the results obtained in the linear case to conclude the nonlinear problem by applying the Right Inverse Function Theorem.

About Organization

Juan Limaco – UFF – Brazil (Coordenador);
Mauro Rincon – UFRJ – Brazil
Max Souza – UFF – Brazil;
Sandra Malta – LNCC – Brazil
Marcelo Cavalcanti – UEM – Brazil;
Rui Almeida – UBI – Portugal
Roxana Lopez – UNMSM – Peru;
Diego Souza – U Sevilla – España;
Mauricio Sepulveda – UdeC – Chile;
Roberto Capistrano – UFPE – Brazil.

Our Partners

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Seminar August 9th of 2023

Seminar August 9th of 2023

por | ago 5, 2023 | Sem categoria

Seminar in EDP and Applied Mathematics

August 9th, 2023 – 14h (Brazil)

Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA 

Youtube Channel

Event

About Seminars

Our Online Seminar is one of the most important events in Brazil, it has been held since August 2020, every Wednesday at 2 pm, Brasília time, with a frequency of 14 days. Two 40-minute lectures are presented in each session. Our speakers are world-renowned mathematicians from Europe, the United States and South America.

Featured Talks & Speakers

Clément Mouhot

University of Cambridge, UK

14:00h – 14:40h

Quantitative Geometric Control in Kinetic Theory

 We will start by a brief introduction to the so-called control theory in analysis of partial differential equations. This theory was initially developed for hyperbolic and parabolic problems (such as propagation of waves and diffusion of heat). However, many fundamental physical equations combine a transport hyperbolic term with a partially dissipative one: kinetic theory in particular presents such structure. We will then discuss a recent work (with F. Hérau, H. Hutridurga and H. Dietert) where we study a class of such equations for which the dissipation on the kinetic variable is active only on part of the spatial domain. We prove quantitative estimates of exponential stabilization under a geometric control condition reminiscent of control theory of wave equations. The proof relies on a new approach to hypocoercivity based on trajectories and quantitative divergence inequalities.

Yuri Thamsten

Vector Trading LLC, Chicago IL, US

14:50h – 15:30h

Optimal trade execution strategies: general models, the strict
problem, and ergodic approximations.

We present a model for optimal execution in which both volatility and liquidity are stochastic.
Our assumption is that a multi-dimensional Markov diffusion drives these processes. In our model, the market is frictional. Particularly, the trader incurs a instantaneous price impact.In this connection, we consider concave-shaped or linear limit order books.

In the regularized setting, meaning we do not necessarily enforce strict execution, we characterize the value function as the unique continuous viscosity solution to the corresponding HJB. We provide this result using appropriate an monotonicity and fixed point arguments.From our method, an iterative numerical algorithm follows for approximating the regularized solution. Then, further proceeding with the monotonicity arguments, we obtain the solution of the optimal strict execution problem as a (singular) limit of its regularized counterparts.Particularly, we guarantee a good numerical approximation for the strict execution problem —
to our knowledge, for the first time in the literature.
Subsequently, we specialize the Markov diffusion to be a fast mean-reverting one. We assess this
hypothesis by using high-frequency financial data. We provide a novel bagging methodology for
estimating the random liquidity model parameters, and also employ noise-robust methods for
estimating the stochastic volatility. Working under this ergodic framework, we derive a leadingorder approximation for the optimal solutions we studied before, and also get a first-order
correction. We provide numerical illustrations and accuracy results for our approximations.

About Organization

Juan Limaco – UFF – Brazil (Coordenador);
Mauro Rincon – UFRJ – Brazil
Max Souza – UFF – Brazil;
Sandra Malta – LNCC – Brazil
Marcelo Cavalcanti – UEM – Brazil;
Rui Almeida – UBI – Portugal
Roxana Lopez – UNMSM – Peru;
Diego Souza – U Sevilla – España;
Mauricio Sepulveda – UdeC – Chile;
Roberto Capistrano – UFPE – Brazil.

Our Partners

Access our channel!

A channel for students, professors, researchers and professionals who wish to deepen their knowledge in EDP and applied mathematics.

Youtube Channel

Contact Us

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