# Exponential and Polynomial Decay in a Thermoelastic-Bresse System with Second Sound

## Abstract

In this paper we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Cattaneo’s law effective in the shear angle displacements. We establish the well-posedness of the system and prove that the system is exponentially stable depending on the parameters of the system. Furthermore, we show that in general, the system is not exponential stable. In this regards, we prove that the solution decays polynomially.

- Authors:

- Djillali Liabes University, Department of Mathematics (Algeria)
- University of Hafr Al-Batin, Mathematics Department (Saudi Arabia)
- King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics (Saudi Arabia)

- Publication Date:

- OSTI Identifier:
- 22750034

- Resource Type:
- Journal Article

- Journal Name:
- Applied Mathematics and Optimization

- Additional Journal Information:
- Journal Volume: 77; Journal Issue: 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; Article Copyright (c) 2016 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; ONE-DIMENSIONAL CALCULATIONS; THERMAL CONDUCTION

### Citation Formats

```
Keddi, Ahmed A., E-mail: ahmedkeddi@gmail.com, Apalara, Tijani A., E-mail: tijani@uohb.edu.sa, and Messaoudi, Salim A., E-mail: messaoud@kfupm.edu.sa.
```*Exponential and Polynomial Decay in a Thermoelastic-Bresse System with Second Sound*. United States: N. p., 2018.
Web. doi:10.1007/S00245-016-9376-Y.

```
Keddi, Ahmed A., E-mail: ahmedkeddi@gmail.com, Apalara, Tijani A., E-mail: tijani@uohb.edu.sa, & Messaoudi, Salim A., E-mail: messaoud@kfupm.edu.sa.
```*Exponential and Polynomial Decay in a Thermoelastic-Bresse System with Second Sound*. United States. doi:10.1007/S00245-016-9376-Y.

```
Keddi, Ahmed A., E-mail: ahmedkeddi@gmail.com, Apalara, Tijani A., E-mail: tijani@uohb.edu.sa, and Messaoudi, Salim A., E-mail: messaoud@kfupm.edu.sa. Sun .
"Exponential and Polynomial Decay in a Thermoelastic-Bresse System with Second Sound". United States. doi:10.1007/S00245-016-9376-Y.
```

```
@article{osti_22750034,
```

title = {Exponential and Polynomial Decay in a Thermoelastic-Bresse System with Second Sound},

author = {Keddi, Ahmed A., E-mail: ahmedkeddi@gmail.com and Apalara, Tijani A., E-mail: tijani@uohb.edu.sa and Messaoudi, Salim A., E-mail: messaoud@kfupm.edu.sa},

abstractNote = {In this paper we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Cattaneo’s law effective in the shear angle displacements. We establish the well-posedness of the system and prove that the system is exponentially stable depending on the parameters of the system. Furthermore, we show that in general, the system is not exponential stable. In this regards, we prove that the solution decays polynomially.},

doi = {10.1007/S00245-016-9376-Y},

journal = {Applied Mathematics and Optimization},

issn = {0095-4616},

number = 2,

volume = 77,

place = {United States},

year = {2018},

month = {4}

}

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