Journal of Mathematical Physics, Analysis, Geometry 2021, vol. 17, No 2, pp. 175-200   https://doi.org/10.15407/mag17.02.175     ( to contents , go back )

### General Decay Result for a Type III Thermoelastic Coupled System with Acoustic Boundary Conditions in the Presence of Distributed Delay

Abdelaziz Limam

Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University, M'sila 28000, Algeria
E-mail: abdelaziz.limam@univ-msila.dz

Yamna Boukhatem

Laboratory of Pure and Applied Mathematics, University of Laghouat, P.O. Box 37G, Laghouat 03000, Algeria
E-mail: y.boukhatem@lagh-univ.dz

Benyattou Benabderrahmane

Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University, M'sila 28000, Algeria
E-mail: benyattou.benabderrahmane@univ-msila.dz

Received February 5, 2020, revised May 13, 2020.

Abstract

In the paper, the general decay of energy solutions for a type III thermoelastic coupled system with distributed delay is studied. The coupling is via the acoustic boundary conditions. Our result is obtained under a class of generality of the relaxation function $g:\mathbb R_+\to \mathbb R_+$ satisfying the inequality $g'(t)\leq -\xi(t) \mathcal H(t)$ for all $t\geq 0$, where $\xi$ and $\mathcal H$ are functions satisfying some specific properties. This work extends previous works with thermoelasticity of type III and improves earlier results in the literature.

Mathematics Subject Classification 2010: 35B40, 74D05, 74F05, 93D15
Key words: thermoelastic effect, acoustic boundary conditions, viscoelastic damping, general decay