Homogenization of attractors for semilinear parabolic equations in domains with spherical traps

Abstract

We consider the attractors associated to a diffusion reaction process through a domain including a high number of spherical obstacles with small holes (“spherical traps”). This process is described by a semilinear parabolic equation, in a domain of ℝ nε n/n−2, ε filled with a periodic set of insulated spheres with small perforations of diameter ɛ n/n − 2,ɛ being the spatial period of the spheres. We are interested in the asymptotical behaviour of the global attractor A ε for the initial problem, as ɛ → 0; and we show that the global attractors A ε tend in a suitable sense to the weak global attractor A for the homogenized model. The corresponding homogenized model is then a system of a parabolic p.d.e. coupled with an o.d.e.