Opuscula Math. 41, no. 4 (2021), 539-570
https://doi.org/10.7494/OpMath.2021.41.4.539

Opuscula Mathematica

# Reaction-diffusion coupled inclusions with variable exponents and large diffusion

Jacson Simsen
Mariza Stefanello Simsen
Petra Wittbold

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.

Keywords: reaction-diffusion coupled systems, variable exponents, attractors, upper semicontinuity, large diffusion.

Mathematics Subject Classification: 35K55, 35K92, 35A16, 35B40, 35B41.

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• Jacson Simsen (corresponding author)
• https://orcid.org/0000-0002-6683-1363
• Universidade Federal de Itajubá, Instituto de Matemática e Computação, Av. BPS n. 1303, Bairro Pinheirinho, 37 500-903, Itajubá - MG - Brazil
• Mariza Stefanello Simsen
• https://orcid.org/0000-0002-2378-2442
• Universidade Federal de Itajubá, Instituto de Matemática e Computação, Av. BPS n. 1303, Bairro Pinheirinho, 37 500-903, Itajubá - MG - Brazil
• Communicated by J.I. Díaz.
• Revised: 2021-06-24.
• Accepted: 2021-06-24.
• Published online: 2021-07-09.