Exponential stability of a type III thermo-porous-elastic system from a new approach in its coupling

Lito E. Bocanegra-Rodríguez; Yony R. Santaria Leuyacc; Paulo N. Seminario-Huertas; Lito E. Bocanegra-Rodríguez; Yony R. Santaria Leuyacc; Paulo N. Seminario-Huertas

doi:10.3934/math.20241084

AIMS Mathematics

2024, Volume 9, Issue 8: 22271-22286. doi: 10.3934/math.20241084

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Research article

Exponential stability of a type III thermo-porous-elastic system from a new approach in its coupling

1.
Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Av. Venezuela S/N, Lima 15081, Peru
2.
Departamento de Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660, Madrid, Spain

Received: 23 May 2024 Revised: 03 July 2024 Accepted: 08 July 2024 Published: 17 July 2024
MSC : 35L15, 35B40, 74F05, 93D20

In this article, we prove the well-posedness and stability of a one-dimensional thermo-porous-elastic system, considering a thermal coupling of the Green and Naghdi types III. In this scenario, we propose a new model where the temperature of the material directly affects the stress tensor of displacements and the equilibrated stress tensor on the volume fractions in the porous medium, thereby generalizing some existing results in the literature on the subject. Additionally, the exponential decay of energy is proven when the evolution equation corresponding to the dynamics of the elastic skeletal structure exhibits frictional-type damping.
- exponential decay,
- well-posedness,
- thermo-porous-elastic systems,
- hyperbolic heat conduction,
- Green-Naghdi heat transfer
Citation: Lito E. Bocanegra-Rodríguez, Yony R. Santaria Leuyacc, Paulo N. Seminario-Huertas. Exponential stability of a type III thermo-porous-elastic system from a new approach in its coupling[J]. AIMS Mathematics, 2024, 9(8): 22271-22286. doi: 10.3934/math.20241084

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Abstract

In this article, we prove the well-posedness and stability of a one-dimensional thermo-porous-elastic system, considering a thermal coupling of the Green and Naghdi types III. In this scenario, we propose a new model where the temperature of the material directly affects the stress tensor of displacements and the equilibrated stress tensor on the volume fractions in the porous medium, thereby generalizing some existing results in the literature on the subject. Additionally, the exponential decay of energy is proven when the evolution equation corresponding to the dynamics of the elastic skeletal structure exhibits frictional-type damping.

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