Convergence of nonautonomous multivalued problems with large diffusion to ordinary differential inclusions

Abstract

In this work we consider a family of nonautonomous partial differential inclusions governed by $ p $-laplacian operators with variable exponents and large diffusion and driven by a forcing nonlinear term of Heaviside type. We prove first that this problem generates a sequence of multivalued nonautonomous dynamical systems possessing a pullback attractor. The main result of this paper states that the solutions of the family of partial differential inclusions converge to the solutions of a limit ordinary differential inclusion for large diffusion and when the exponents go to $ 2 $. After that we prove the upper semicontinuity of the pullback attractors.