GLOBAL ATTRACTORS OF NONLOCAL REACTION DIFFUSION EQUATIONS WITH EXPONENTIAL NONLINEARITIES

Abstract

In this paper, we investigate the existence, uniqueness, and continuity of weak solutions with respect to initial values for a nonlinear parabolic equation of reactiondiffusion nonlocal type by an application of the Faedo-Galerkin approximation and AubinLions- Simon compactness results. The nonlocal quantity appears in the diffusion coefficient. Moreover, we deal with a new class of nonlinearities which is no restriction on the growth of the nonlinearities. The long -time behaviour of solutions to that problem is considered via the concept of global attractors for the associated semigroups.