Título: Weakly coupled elliptic systems with cooperative or competitive interactions: an overview
Palestrante: Hugo Tavares (Faculdade de Ciências da Universidade de Lisboa)
Data: 19/07/2019
Horário: 10h
Local: Sala C116
Resumo: In this talk, we will deal with systems of stationary reaction-diffusion equations where the interaction between different components is either cooperative or competitive. Our aim will be to explain some of the relevant questions that can be asked for each type of interaction, explaining as well the motivations for its study. We will survey some of the results proved in the last few years, discussing in general the existence and characterization of positive solutions. Furthermore, we will explain how a strong competition induces a phase separation phenomenon and gives rise to a free boundary problem.
In the last part of the talk, we will consider nonlocal interaction terms between the components. We will highlight some of the similarities and differences between the local and the nonlocal cases, showing some recent results in the nonlocal one.
Titulo: Null controllability of the structurally damped wave equation with a moving control
Palestrante: Lionel Rosier (MINES ParisTech, França)
Data: 10/07/2019
Horário: 12h
Local: Instituto de Matemática – Bloco C – Sala C116 – Ilha do Fundão
Resumo: We investigate the null controllability of the wave equation with a Kelvin-Voigt damping. It is well known that the null controllability fails if the control region is fixed and strictly included in the space domain. We consider here a distributed control supported in a moving domain. We shall review recent results obtained by the speaker on this issue: (i) in dimension one (with P. Martin and P. Rouchon); (ii) in dimension N (with F. W. Chaves-Silva and E. Zuazua); (iii) in dimension two, with sharp geometric conditions (with P. Guzman).
Título: Spectral Theory Approach for a Class of Indefinite Variational Problems
Palestrante: Mayra Soares (PUC-Rio)
Data: 22/05/2019 (quarta feira)
Horário: 12h
Sala: Instituto de Matemática – Bloco C – Sala C116 – Ilha do Fundão
Resumo: An abstract linking theorem for Cerami sequences is developed with the purpose of handling indefinite problems by variational approach, especially nonlinear Schrödinger equations with sign-changing potentials and asymptotically linear nonlinearities.
In order to find a nontrivial solution to the problem under discussion, we apply the abstract result to the associated indefinite functional and obtain a nontrivial critical point to such a functional. This critical point is going to be a weak solution to the problem, as desired.
Spectral theory is the main tool used in this work. Exploiting spectral properties of the elliptic operator associated to the problem in question, it enables to establish a linking structure on the Hilbert space where the mentioned critical points are sought.
É com grande satisfação que anunciamos o 1° Seminário Integrado de Análise e EDP, coordenado conjuntamente pela PUC-Rio, UFF e UFRJ.
A primeira edição do evento ocorrerá no IM-UFRJ no dia 31/05, na sala C116, às 14h. A programação incluirá três palestras:
14h - 14h50: Max Souza (UFF)
14h50 - 15h40: Boyan Sirakov (PUC-Rio)
16h00 - 16h50: Milton Lopes (UFRJ)
Palestra: Limites newtonianos para escoamentos incompressíveis em domínios com fronteira
Palestrante: Milton da Costa Lopes Filho (UFRJ)
Data: 24/04/2019 (quarta-feira)
Horário: 12h
Sala: Instituto de Matemática – Bloco C – Sala C116 – Ilha do Fundão
Resumo: Descrevemos uma série de resultados acerca de limites dos modelos Euler-alfa e de fluídos de grau dois para as equações de Euler incompressíveis com condições de fronteira sem deslizamento e com condições de fricção tipo Navier.
