Convergence of quasilinear parabolic equations to semilinear equations

Flank D. M. Bezerra; Jacson Simsen; Mariza Stefanello Simsen

doi:10.3934/dcdsb.2020258

Article Contents

2021, Volume 26, Issue 7: 3823-3834. Doi: 10.3934/dcdsb.2020258

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Convergence of quasilinear parabolic equations to semilinear equations

1.
Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa - PB, Brazil
2.
Instituto de Matemática e Computação, Universidade Federal de Itajubá, Av. BPS n. 1303, Bairro Pinheirinho, 37500-903, Itajubá - MG, Brazil

^* Corresponding author: Jacson Simsen
^* Corresponding author: Jacson Simsen

Received: March 31, 2020

Revised: June 30, 2020

Early access: August 2020

Published: July 2021

J. Simsen was partially supported by the Brazilian research agency FAPEMIG - Process PPM 00329-16

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Abstract

In this work we consider a family of reaction-diffusion equations with variable exponents reaching as a limit problem a semilinear equation. We provide uniform estimates for the solutions and we prove that the solutions of the family of quasilinear equations with variable exponents converge to the solution of a limit semilinear equation when the exponents go to 2. Moreover, the robustness of the global attractors is also studied.

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Mathematics Subject Classification: Primary:35B40, 35B41, 35K57;Secondary:35K59.

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References

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