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Research Article | Open Access

Growth of solutions with L 2 ( p + 2 ) -norm for a coupled nonlinear viscoelastic Kirchhoff equation with degenerate damping terms

Abdelbaki Choucha1,2, Muajebah Hidan3, Bahri Cherif4, Sahar Ahmed Idris5( )
Department of Mathematics, Faculty of Exact Sciences, University of El Oued, Algeria
Department of Matter Sciences, Faculty of Sciences, Amar Teleji Laghouat University, Algeria
Mathematics Department, Faculty of Science, King Khalid University, Abha 61471, Saudi Arabia
Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Kingdom of Saudi Arabia
College of Industrial Engineering, King Khalid University, Abha 62529, Saudi Arabia
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Abstract

In this work, we consider a coupled nonlinear viscoelastic Kirchhoff equations with degenerate damping, dispersion and source terms. Under suitable hypothesis, we will prove that when the initial data are large enough (in the energy point of view), the energy grows exponentially and thus so the L 2 ( p + 2 ) -norm.

Keywords

viscoelastic equationexponential growthdegenerate damping term
CLC number: 35B40, 35L45, 93D15, 93D20

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 371-383
DOI: 10.3934/math.2022025

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Cite this article:
Choucha A, Hidan M, Cherif B, et al. Growth of solutions with L 2 ( p + 2 ) -norm for a coupled nonlinear viscoelastic Kirchhoff equation with degenerate damping terms. AIMS Mathematics, 2022, 7(1): 371-383. https://doi.org/10.3934/math.2022025

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Received: 01 September 2021
Accepted: 10 October 2021
Published: 15 January 2022
©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)