Reaction-diffusion coupled inclusions with variable exponents and large diffusion

Abstract

This work concerns the study of asymptotic behavior of coupled systems of $p(x)$-Laplacian differential inclusions. We obtain that the generalized semiflow generated by the coupled system has a global attractor, we prove continuity of the solutions with respect to initial conditions and a triple of parameters and we prove upper semicontinuity of a family of global attractors for reaction-diffusion systems with spatially variable exponents when the exponents go to constants greater than 2 in the topology of $L^{\infty}(\Omega)$ and the diffusion coefficients go to infinity.