Nonlocal evolution equations in perforated domains

Abstract

In this paper, we study a nonlocal evolution equation posed in perforated domains. We consider problems of the form with x in a perturbed domain . We think about Ωε as a fixed set Ω from where we have removed the subset Aε that we call the holes. Moreover, we take J as a nonsingular kernel. Assuming weak convergence of the holes, specifically, under the assumption that the characteristic function of Ωε has a weak limit, weakly∗ in L∞(Ω) as ε→0, we analyze the limit of the solutions proving a nonlocal homogenized evolution equation.