Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution

Abstract

In this paper, the existence of solution for a p-Laplacian parabolic equation with nonlocal diffusion is established. To do this, we make use of a change of variable which transforms the original problem into a nonlocal one but with local diffusion. Since the uniqueness of solution is unknown, the asymptotic behaviour of the solutions is analysed in a multi-valued framework. Namely, the existence of the compact global attractor in L2(Ω) is ensured.