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

Well-posedness and Stability for a Moore-Gibson-Thompson Equation with Internal Distributed Delay

Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 693--703 | DOI:10.5890/DNC.2021.12.009

Abdelkader Braik$^1$, Abderrahmane Beniani$^2$, Khaled Zennir$^3$

$^1$ Department of Sciences and Technology, University of Hassiba Ben Bouali, Chlef, Algeria

$^2$ Department of Mathematics, BP 284, University Centre BELHADJ Bouchaib Ain Tmouchent 46000, Algeri

$^3$ Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia

Abstract

In this work, we consider the Moore-Gibson-Thompson equation with distributed delay. We prove, under an appropriate assumptions and a smallness conditions on the parameters $\alpha$, $\beta$, $\gamma$ and $\mu$, that this problem is well-posed and then by introducing suitable energy and Lyapunov functionals, the solution of \eqref{p1} and \eqref{p2} decays to zero as $t$ tends to infinity.

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