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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Global Existence and General Decay of a Weakly Nonlinear Damped Timoshenko System of Thermoelasticity of Type III with Infinite Memory

Journal of Applied Nonlinear Dynamics 11(1) (2022) 195--215 | DOI:10.5890/JAND.2022.03.012

Mohamed Houasni$^{1,3}$ , Salah Zitouni$^{2}$, Abdelhak Djebabla$^{3}$

$^1$ Facult\'{e} des Sciences et de la Technologie, Universit\'{e} DBKM, Alg\'{e}rie

$^{2}$ Department of Mathematics, Souk Ahras Univ, P.O. Box 1553, Souk Ahras, 41000, Algeria

$^{3}$ Laboratory of Applied Mathematics, University Badji Mokhtar, P.O. Box 12, 23000 Annaba, Algeria

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Abstract

In this work, we consider a one-dimensional Timoshenko system of thermoelasticity of type III with infinite memory damped by weakly nonlinear feedbacks. Under suitable conditions, we establish the well-posedness of the problem using semigroups theory, and a general stability estimates using the multiplier method with no growth assumption on $f$ at the origin and without assuming equal or nonequal speeds of propagation of waves which is mentioned in numerous works (e.g. \cite{ayadi,chen,Fareh,jh,hao,masap}). Our results show that the damping effect leads to general decay rate for the energy function and also remove the necessity of the assumption on equal speeds which has been imposed in the prior literature.

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