Opuscula Mathematica
Opuscula Math. 41, no. 4 (2021), 539-570

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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About the authors ▼
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
Petra Wittbold
https://orcid.org/0000-0001-5440-0032
Universität of Duisburg-Essen, Fakultät für Mathematik, Thea-Leymann-Str. 9, 45 127 Essen, Germany
About the article ▼
Communicated by J.I. Díaz.
Received: 2021-03-23.
Revised: 2021-06-24.
Accepted: 2021-06-24.
Published online: 2021-07-09.
Cite this article as ▼
Jacson Simsen, Mariza Stefanello Simsen, Petra Wittbold, Reaction-diffusion coupled inclusions with variable exponents and large diffusion, Opuscula Math. 41, no. 4 (2021), 539-570, https://doi.org/10.7494/OpMath.2021.41.4.539.
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