GLOBAL ATTRACTORS OF NONLOCAL REACTION DIFFUSION EQUATIONS WITH EXPONENTIAL NONLINEARITIES

Tóm tắt

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.