On uniqueness and monotonicity of solutions of non-local reaction diffusion equation

Abstract

This article deals with the uniqueness and the behavior of solutions of non-local reaction diffusion equations. Since these equations share many properties with the usual reaction diffusion model, such as a form of maximum principle and the translation invariance, uniqueness and monotone behavior for the solution, as in the usual case, are expected. I present an elementary proof of this monotone behavior. The proof essentially uses techniques based on the maximum principle and the sliding method. © 2005 Springer-Verlag.