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)
  • ORCID iD 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
  • ORCID iD 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.
  • Received: 2021-03-23.
  • Revised: 2021-06-24.
  • Accepted: 2021-06-24.
  • Published online: 2021-07-09.
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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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