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Reaction-diffusion coupled inclusions with variable exponents and large diffusion

Simsen Jacson, Stefanello Simsen Mariza, Wittbold Petra

Opuscula Mathematica

2021

Vol. 41, no. 4

539--570

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 [formula] and the diffusion coefficients go to infinity.