[: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.[:]