Título: Boundary homogenization problems with high contrasts: the elasticity system & the local problems
Data: 27/01/2023
Horário: 11:00h
Local: C-116
Palestrante: María Eugenia Pérez Martínez (Universidad de Cantabria)
Resumo: We consider the homogenization problem for the elasticity operator posed in a bounded domain of the upper half-space, a part of its boundary being in contact with the plane. We assume that this surface is free outside small regions in which we impose Robin-Winkler boundary conditions linking stresses and displacements by means of a symmetric and positive definite matrix and a reaction parameter. These small regions are periodically placed along the plane while its size is much smaller than the period. We look at the asymptotic behaviour of spectrum and provide all the possible spectral homogenized problems depending on certain asymptotic relations between the period, the size of the regions and the reaction-parameter. We state the convergence of the eigenelements, as the period tends to zero, which deeply involves the corresponding microscopic stationary problems obtained by means of asymptotic expansions.
We compare results and techniques with those for the Laplace operator and outline some possible extensions (under consideration) of the problem.
Some references:
[1] D. Gómez, S.A. Nazarov, ; M.-E. Pérez-Martínez. Asymptotics for spectral problems with rapidly alternating boundary conditions on a strainer Winkler foundation. Journal of Elasticity, 2020, V. 142, p. 89-120.
[2] D. Gómez, S.A. Nazarov ; M.-E. Pérez-Martínez. Spectral homogenization problems in linear elasticity with large reaction terms concentrated in small regions of the boundary. In: Computational and Analytic Methods in Science and Engineering. Birkäuser, Springer, N.Y., 2020, pp. 121-143
[3] D. Gómez; M.-E. Pérez-Martínez. Boundary homogenization with large reaction terms on a strainer-type wall. Z. Angew. Math. Phys. Vol. 73, 28p 2022.
[4] M.-E. Pérez-Martínez. Homogenization for alternating boundary conditions with large reaction terms concentrated in small regions. In: Emerging problems in the homogenization of Partial Differential Equations. ICIAM2019 SEMA SIMAI Springer Series 10, 2021, pp. 37-57.
Todas as informações sobre o seminário se encontram no site. Acesse clicando AQUI.
Título: Stability of Mkdv Breathers on The Half-Line
Palestrante: Márcio Cavalcante (UFAL)
Data: 18/01/2023
Horário: 12:00h
Local: C-116
Resumo: In this talk I will discuss the stability problem for mKdV breathers on the left half-line. We are able to show that leftwards moving breathers, initially located far away from the origin, are strongly stable for the problem posed on the left half-line, when assuming homogeneous boundary conditions. The proof involves a Lyapunov functional which is almost conserved by the mKdV flow once we control some boundary terms which naturally arise. Also, recent results about orbital and asymptotic stability of solitons on the positive half-line will be discussed. This is a joint work with Miguel Alejo and Adán Corcho.
Título: Rapid stabilization of linearized water waves and Fredholm backstepping for critical operators
Data: 29/11/2022
Horário: 14:00h
Local: Sala C-119
Palestrante: Ludovick Gagnon (Université de Lorraine, CNRS, Inria équipe SPHINX)
Resumo: The backstepping method has become a popular way to design feedback laws for the rapid stabilization of a large class of PDEs. This method essentially reduces the proof of exponential stability to the existence and invertibility of a transformation. Initially applied with a Volterra transformation, the Fredholm alternative, introduced by Coron and Lü, allows to overcome some existence issues for the Volterra transformation. This new approach also has the advantage of having a systematic methodology, but the methods known until now were only applicable to differential operators D_x^a with a>3/2. In this talk, we present the duality/compactness method to surmount this threshold and show that the Fredholm-type backstepping method applies for anti-adjoint operators i |D_x|^a, with a >1. We will demonstrate the application of this result for the rapid stabilization of the linearized water waves equation.
Título: Models of mosquito population control strategies for fighting against arboviruses
Palestrante: Michel Duprez (Inria, Université de Strasbourg, ICUBE)
Data: 30/11/2022
Horário: 12:00h
Local: Sala C-116
Resumo: In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, Aedes mosquitoes in this case. Among possible actions, a technique consist in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique). This talk is devoted to studying the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing the dynamic of a mosquitoes population, we will study the control problem and introduce the cost function standing for sterile insect technique. In a second step, we will consider a model with several patchs modeling the spatial repartition of the population. Then, we will establish some properties of these two optimal control problems. Finally, we will illustrate our results with numerical simulations.
Título: Magic Functions
Palestrante: Felipe Gonçalves (IMPA)
Data: 19/10/2022
Horário: 12:00h
Local: Sala C-116
Resumo: We will talk about some of the challenging problems in different areas of mathematics that were solved by constructing certain "magic" functions with constraints on physical and/or frequency space (we shall focus slightly on the bandlimited case). The talk will be based entirely on examples, one of which is the sphere packing problem (its solution awarded the Fields medal to the Ukrainian female mathematician M. Viazovska).
Todas as informações sobre o seminário se encontram no site, clique AQUI e acesse.
