Asymptotic behaviour for a diffusion equation governed by nonlocal interactions.

Abstract

In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the parabolic problem $L^{\infty }$ estimates of solution based on using the Moser iterations and existence of global attractor. We finish our study by the issue of asymptotic behaviour in some cases when $t\to \infty$.

References in corpus (1)

• Regularity theory for fully nonlinear integro-differential equations