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

Abdelbaki Choucha; Muajebah Hidan; Bahri Cherif; Sahar Ahmed Idris; Abdelbaki Choucha; Muajebah Hidan; Bahri Cherif; Sahar Ahmed Idris

doi:10.3934/math.2022025

AIMS Mathematics

2022, Volume 7, Issue 1: 371-383. doi: 10.3934/math.2022025

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

1.
Department of Mathematics, Faculty of Exact Sciences, University of El Oued, Algeria
2.
Department of Matter Sciences, Faculty of Sciences, Amar Teleji Laghouat University, Algeria
3.
Mathematics Department, Faculty of Science, King Khalid University, Abha 61471, Saudi Arabia
4.
Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Kingdom of Saudi Arabia
5.
College of Industrial Engineering, King Khalid University, Abha 62529, Saudi Arabia

Received: 01 September 2021 Accepted: 10 October 2021 Published: 13 October 2021
MSC : 35B40, 35L45, 93D15, 93D20

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.
- viscoelastic equation,
- exponential growth,
- degenerate damping term
Citation: Abdelbaki Choucha, Muajebah Hidan, Bahri Cherif, Sahar Ahmed Idris. Growth of solutions with $ L^{2(p+2)} $-norm for a coupled nonlinear viscoelastic Kirchhoff equation with degenerate damping terms[J]. AIMS Mathematics, 2022, 7(1): 371-383. doi: 10.3934/math.2022025

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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.

References

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