Dynamics of parabolic equations in domains with a small hole II. Continuity of the attractors - Tavares–Lima, E. A. [UNESP]; Lozada-Cruz, G. [UNESP] (Elsevier, 2024)
In this paper we study the asymptotic dynamics for a class of semilinear parabolic problems with Dirichlet boundary conditions in domains with a small hole of size proportional to a positive parameter ε. In other words, we prove that the family of attractors behaves continuously as ε→0. We will also provide the convergence rates in terms of the parameter.
Keywords: Attractors; Domain with hole; Lower and upper semi-continuity; Parabolic equations