GLOBAL ATTRACTOR FOR A NONLOCAL -LAPLACE PARABOLIC EQUATION WITH NONLINEARITY OF ARBITRARY ORDER

Abstract

In this paper  we consider a nonlocal -Laplace parabolic equation depending on the  norm of the gradient with nonlinearity of arbitrary order. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence and regularity of a global attractor for the associated semigroup. The main novelty of our results is that no restriction on the upper growth of the nonlinearity is imposed.