Seminar in EDP and Applied Mathematics

June 14, 2023 – 14h (Brazil)

Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA

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

Juan Casado

Universidad de Sevilla (Spain)

14:00h – 14:40h

The minimization and maximization of the first eigenvalue for a two-phase material.

We study a classical problem in optimal design. Ir consists in minimizing or maximizing the first eigenvalue of the Dirichlet problem for a diffusion operator corresponding to a two-phase material. The amount of each of the materials is prescribed. We show that these problems have only solution in very few cases, which we characterize. Thus, it is needed to work with a relaxed formulation. We get some results about the uniqueness and regularity of the solutions of such relaxed problem and some numerical results.

Swann Marx

CNRS-LS2N (Nantes)

14:50h – 15:30h

Singular perturbation analysis for a coupled KdV-ODE system

This talk will be about the asymptotic analysis of a Korteweg-De Vries equation coupled with an ODE. An asymptotic analysis will be proposed by using Lyapunov functionals. Furthermore, if one assumes that the Korteweg-de Vries equation is much faster than the ODE, weaker stability conditions can be obtained thanks a singular perturbation analysis. The singular perturbation method consists in approximating a coupled system with different time-scales into two approximated systems, for which the asymptotic stability conditions is easier. For ODEs, it is known that, as soon as the two approximated systems are asymptotically stable, then the full-system is stable if the fast system is sufficiently fast. During the talk, it will be proved that such a theory works for the special case of a Korteweg-de Vries coupled with an ODE, but some counter-examples will be given for some other PDEs (namely, transport equations). It is joint work with Eduardo Cerpa.

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.