Exponential stability of a porous thermoelastic system with Gurtin–Pipkin thermal law

被引：0
作者：
Abdelfeteh Fareh
机构：
[1] University of El Oued,Laboratory of Operators Theory and PDEs: Foundations and Applications, Faculty of Exact Sciences
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2022年 / 116卷
关键词：
Porous thermoelasticity; Gurtin–Pipkin law; Contraction semigroup; Exponential stability; 35B40; 47D03; 74D05; 74F05;
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摘要：
In this paper we consider a one-dimensional porous thermoelastic system with hereditary heat conduction. Existence and uniqueness of a solution are obtained by the use of Lumer–Phillips and Lax–Milgram theorems. Using a semigroup approach, we prove under some assumptions on the derivative of the heat-flux kernel, that the solution of the system decays exponentially without any assumption on the wave speeds. This result extends the results of Messaoudi and Fareh (Discrete Contin Dyn Syst B 20(2):599–612, 2015) and Muñoz Rivera and Quintanilla (J Math Anal Appl 338:1296–1309, 2008) to a more general case of heat conduction.
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