On the limit of solutions for a reaction-di¤usion equation containing fractional Laplacians

Abstract

A kind of nonlocal reaction-di¤usion equations on an unbounded domain containing a frac- tional Laplacian operator is analyzed. To be precise, we prove the convergence of solutions of the equation governed by the fractional Laplacian to the solutions of the classical equation governed by the standard Laplacian, when the fractional parameter grows to 1. The existence of global attractors is investigated as well. The novelty of this paper is concerned with the convergence of solutions when the fractional parameter varies, which, as far as the authors are aware, seems to be the rst result of this kind of problems in the literature.