ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

The Effect of Damping Terms on Decay Rate for System of Three Nonlinear Wave Equations with Weak-Memories

Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 635--647 | DOI:10.5890/DNC.2021.12.005

Derradji Guidad$^1$, Khaled Zennir$^{2,3}$ , Abdelhak Berkane$^4$, Mohamed Berbiche$^1$

$^1$ Department of Mathematics, College of Sciences, University Mohamed Khider- Biskra, Algeria

$^2$ Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia

$^3$ Laboratoire de Math'ematiques Appliqu'ees et de Mod'elisation, Universit'e 8 Mai 1945 Guelma. B.P. 401 Guelma 24000 Alg'erie

$^4$ Departement de Math'ematiques, Facult'e des sciences exact, Universit'e freres Mentouri-Constantine, Algeria

Abstract

In this paper, we consider a very important problem from the point of view of application in sciences and engineering. A system of three wave equations having a different damping effects in an unbounded domain with strong external forces. Using the Faedo-Galerkin method and some energy estimates, we will prove the existence of global solution in $\mathbb{R}^n$ owing to to the weighted function. By imposing a new appropriate conditions, which are not used in the literature, with the help of some special estimates and generalized Poincar\'e's inequality, we obtain an unusual decay rate for the energy function.

Acknowledgments

The authors expresses sincerely thanks to the referees for their constructive comments and suggestions that helped to improve this paper. \begin{thebibliography}{999}

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