Homogenization of attractors to reaction-diffusion system in a medium with random obstacles
Kuanysh Abdrakhmanovich Bekmaganbetov, Gregory Aleksandrovich Chechkin, Vladimir Victorovich Chepyzhov · Discrete and Continuous Dynamical Systems · 2024
A reaction-diffusion system in a domain with randomly located obstacles was considered. When studying the problem, we sat the homogeneous Dirichlet condition on the outer boundary of the domain and the Neumann condition on the boundary of the cavities. Under such assumptions, it was proven that random trajectory attractors of this system with random coefficients converge in some weak topology to the deterministic trajectory attractor of a homogenized reaction-diffusion system with deterministic coefficients in a homogeneous domain without obstacles. In the case of uniqueness, we obtained weak convergence of random global attractors to a deterministic global attractor.Bibliography: 19 titles.