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Research Article | Open Access

Destruction of solutions for class of wave p ( x ) −bi-Laplace equation with nonlinear dissipation

Khaled Zennir1,2, Abderrahmane Beniani3, Belhadji Bochra4, Loay Alkhalifa1( )
Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia
Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma, B.P. 401, Guelma 24000, Algeria
EDPs Analysis and Control Laboratory, Department of Mathematics, BP 284, University Ain Témouchent BELHADJ, Bouchaib 46000, Algeria
Laboratoire de Mathématiques et Sciences Appliquées, Université de Ghardaia, BP 455, Ghardaia 47000, Algeria
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Abstract

An initial value problem is considered for the nonlinear dissipative wave equation containing the p ( x )-bi-Laplacian operator. For this problem, sufficient conditions for the blow-up with nonpositive initial energy of a generalized solution are obtained in finite time where a wide variety of techniques are used.

Keywords

Sobolev spaces with variable exponentsp(x)-bi-Laplaceblow-upinitial energy
CLC number: 35B35, 35G05, 35Q70, 45D05, 74D99

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AIMS Mathematics
Volume 8 Issue 1,
January 2023
Pages 285-294
DOI: 10.3934/math.2023013

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Cite this article:
Zennir K, Beniani A, Bochra B, et al. Destruction of solutions for class of wave p ( x ) −bi-Laplace equation with nonlinear dissipation. AIMS Mathematics, 2023, 8(1): 285-294. https://doi.org/10.3934/math.2023013

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Received: 03 August 2022
Revised: 15 September 2022
Accepted: 22 September 2022
Published: 15 January 2023
©2023 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)