Nonlocal evolution problems in thin domains

Abstract

In this paper, we consider parabolic nonlocal problems in thin domains. Fix and consider be the solution to with initial condition and a kernel of the form with J non-singular. This corresponds (via a simple change of variables) to the usual nonlocal evolution problem , in the thin domain . Our main result says that there is a limit as of the solutions to our problem and that this limit, when we take its mean value in the -direction, is a solution to a limit nonlocal problem in the projected set .