2018 Thematic Program (II)

Dynamics of reaction-diffusion equations under perturbations of the domain


June 29, 2018  11:00-12:00

W303  School of Mathematics, Sichuan University

[lecture XIII]Jose M. Arrieta0629-01.png


Jose M. Arrieta (Universidad Complutense de Madrid)


We analyze the behavior of the asymptotic dynamics of dissipative reaction-diffusion equations with Neumann boundary conditions when the domain where the equation is posed undergoes certain perturbation. We will focus on the behavior of the stationary solutions, their local unstable manifolds and the attractors. We may consider "regular" perturbations of the domain for which the spectra of the Laplace operator behaves continuously. In this case, it turns out that If all the equilibria of the unperturbed system are nondegenerate (hyperbolic), both the equilibria and the local unstable manifolds of the equilibria behave continuously under the perturbation of the domain. Hence, exploiting the gradient properties of the flow we will show that the "attractors’"behave continuously under these perturbations. We may also consider more "drastic" perturbations like "thin domains"or "dumbbell domains" for which similar results can be obtained. If time allows, we will go over some recent results on the estimates on the distance of the attractors for the case of thin domains.


Kening Lu (Sichuan University)

Weinian Zhang (Sichuan University)

Wen Huang (Sichuan University)

Zeng Lian (Sichuan University)

Xiaohu Wang (Sichuan University)

Linfeng Zhou (Sichuan University)

Jun Shen (Sichuan University)


Tianyuan Mathematical Center in Southwest China

School of Mathematics, Sichuan University