Attractors of reaction-diffusion equations with nonmonotone nonlinearity

Abstract

In this paper we study the existence of global compact attractors for nonlinear parabolic equations of reaction-diffusion type. The studied equations are generated by a difference of subdifferential maps and are not assumed to have a unique solution for each initial state. Applications are given to inclusions modelling combustion in porous media and processes of transmission of electrical impulses in nerve axons.