Convergence of nonautonomous multivalued problems with large diffusion to ordinary differential inclusions (2020), Communications On Pure And Applied Analysis 19 (4): 2347–2368.

[:es]Jacson Simsen (Universidade Federal de Itajubá), Mariza Stefanello Simsen (Universidade Federal de Itajubá) and José Valero (University Miguel Hernández of Elche). 

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.

Keywords: Differential inclusions; large diffusion, reaction-diffusion equations; pullback attractors; nonautonomous dynamical systems; multivalued dynamical systems; plaplacian; variable exponent; upper semicontinuity.[:]