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Journal of Applied Nonlinear Dynamics 11(1) (2022) 153--170 | DOI:10.5890/JAND.2022.03.009

Djamel Ouchenane$^1$ , Khaled Zennir$^{2, 3}$, Derradji Guidad$^4$

$^1$ Laboratory of pure and applied Mathematics , Amar Teledji Laghouat University, Algeria

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

$^3$ Laboratoire de Mathematiques Appliquees et de Modelisation, Universite 8 Mai 1945 Guelma. B.P. 401 Guelma 24000 Algerie

$^4$ Department of Mathematics, College of Sciences, Mohamed Khider Biskra University, Algeria

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Abstract

As a continuity to the study by M. M. Al-Gharabli et al. in [1], we consider a one-dimensional porous thermoelastic system with second sound, distributed delay term and nonlinear feedback. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result, using some properties of convex functions and the multiplier method. Our result is obtained under suitable assumption on delay without imposing any restrictive growth assumption on the damping term.

Acknowledgments

The authors are highly grateful to the anonymous referee for his/her valuable comments and suggestions for the improvement of the paper. This research work is supported by the General Direction of Scientific Research and Technological Development (DGRSDT), Algeria.

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