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Research Article | Open Access

Global existence and asymptotic behavior for a viscoelastic Kirchhoff equation with a logarithmic nonlinearity, distributed delay and Balakrishnan-Taylor damping terms

Abdelbaki Choucha1,2, Salah Boulaaras3( ), Asma Alharbi3
Laboratory of Operator Theory and PDEs: Foundations and Applications, Department of Mathematics, Faculty of Exact Sciences, University of El Oued, Algeria
Department of Mathematics, Faculty of Sciences, Amar Teledji Laghouat University, Algeria
Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Saudi Arabia
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Abstract

A nonlinear viscoelastic Kirchhoff-type equation with a logarithmic nonlinearity, Balakrishnan-Taylor damping, dispersion and distributed delay terms is studied. We establish the global existence of the solutions of the problem and by the energy method we prove an explicit and general decay rate result under suitable hypothesis.

Keywords

Kirchhoff equationexponential decaydistributed delay termviscoelastic termlogarithmic nonlinearity
CLC number: 35B40, 35L20, 35L70, 93D20

References

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 4517-4539
DOI: 10.3934/math.2022252

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Choucha A, Boulaaras S, Alharbi A. Global existence and asymptotic behavior for a viscoelastic Kirchhoff equation with a logarithmic nonlinearity, distributed delay and Balakrishnan-Taylor damping terms. AIMS Mathematics, 2022, 7(3): 4517-4539. https://doi.org/10.3934/math.2022252

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Received: 31 August 2021
Revised: 12 December 2021
Accepted: 16 December 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)