Exponential stability for porous thermoelastic systems with Gurtin-Pipkin flux

Authors

  • Jianghao Hao Shanxi Univ., Taiyuan, Shanxi 030006, China
  • Jing Yang Shanxi Univ., Taiyuan, Shanxi 030006, China

DOI:

https://doi.org/10.58997/ejde.2023.44

Keywords:

Gurtin-Pipkin flux; porous thermoelastic system; semigroup theory; exponential stability.

Abstract

In this article, we study the stability of a porous thermoelastic system with Gurtin-Pipkin flux. Under suitable assumptions for the derivative of the heat flux relaxation kernel, we establish the existence and uniqueness of solution by applying the semigroup theory, and prove the exponential stability of system without considering the wave velocity by the means of estimates of the resolvent

For more information see https://ejde.math.txstate.edu/Volumes/2023/44/abstr.html

References

M. E. Gurtin, A. C. Pipkin; A general theory of heat conduction with nite wave speeds, Archive for Rational Mechanics and Analysis, 31(2) (1968), 113-126.

P. S. Casas, R. Quintanilla; Exponential decay in one-dimensional porous-thermo-elasticity, Mechanics Research Communications, 32(6) (2005), 652-658.

T. A. Apalara; On the stabilization of a memory-type porous thermoelastic system, Bulletin of the Malaysian Mathematical Sciences Society, 43(2) (2020), 1433-1448.

A. M. Al-Mahdi, M. M. Al-Gharabli, S. A. Messaoudi; New general decay of solutions in a porous-thermoelastic system with in nite memory, Journal of Mathematical Analysis and Applications, 500(1) (2021), 1-19.

A. Maga~na, R. Quintanilla; On the time decay of solutions in one-dimensional theories of porous materials, International Journal of Solids and Structures, 43(11-12) (2006), 3414-3427.

P. S. Casas, R. Quintanilla; Exponential stability in thermoelasticity with microtemperatures, International Journal of Engineering Science, 43(1-2) (2005), 33-47.

P. X. Pamplona, J. E. Mu~noz Rivera, R. Quintanilla; Stabilization in elastic solids with voids, Journal of Mathematical Analysis and Applications, 350(1) (2009), 37-49.

A. Djebabla, A. Choucha, D. Ouchenane, K. Zennir; Explicit stability for a porous thermoe-lastic system with second sound and distributed delay term, International Journal of Applied and Computational Mathematics, 7(2) (2021), 1-16.

J. H. Hao, P. P. Wang; Asymptotical stability for memory-type porous thermoelastic system of type III with constant time delay, Mathematical Methods in the Applied Sciences, 39(13) (2016), 3855-3865.

R. Quintanilla; Exponential stability for one-dimensional problem of swelling porous elastic soils with fluid saturation, Journal of Computational and Applied Mathematics, 145(2) (2002), 525-533.

J. E. Mu~noz Rivera, R. Racke; Mildly dissipative nonlinear Timoshenko systems-global existence and exponential stability, Journal of Mathematical Analysis and Applications, 276(1) (2002), 248-278.

S. A. Messaoudi, A. Fareh; General decay for a porous thermoelastic system with memory: The case of equal speeds, Nonlinear Analysis. Theory, Methods & Applications, 74(18) (2011), 6895-6906.

S. A. Messaoudi, A. Fareh; General decay for a porous thermoelastic system with memory: The case of nonequal speeds, Acta Mathematica Scientia, 33(1) (2013), 23-40.

D. S. Almeida J unior, M. L. Santos, J. E. Mu~noz Rivera; Stability to 1-D thermoelastic Timoshenko beam acting on shear force, Zeitschrift fur Angewandte Mathematik und Physik, 65(6) (2014), 1233-1249.

T. A. Apalara; General stability of memory-type thermoelastic Timoshenko beam acting on shear force, Continuum Mechanics and Thermodynamics, 30(2) (2018), 291-300.

L. H. Fatori, J. E. Mu~noz Rivera; Rates of decay to weak thermoelastic Bresse system, IMA Journal of Applied Mathematics, 75(6) (2010), 881-904.

F. Djellali, S. Labidi, F. Taallah; Existence and energy decay of a Bresse system with thermoelasticity of type III, Zeitschrift fur Angewandte Mathematik und Physik, 73(1) (2022), 1-25.

A. Fareh, S. A. Messaoudi; Energy decay for a porous thermoelastic system with thermoelasticity of second sound and with a non-necessary positive de nite energy, Applied Mathematics and Computation, 293 (2017), 493-507.

H. D. Fern andez-Sare, R. Racke; On the stability of damped Timoshenko system Cattaneo versus Fourier law, Archive for Rational Mechanics and Analysis, 194(1) (2009), 221-251.

M. L. Santos, D. S. Almeida Junior, J. E. Mu~noz Rivera; The stability number of the Timoshenko system with second sound, Journal of Di erential Equations, 253(9) (2012), 2715-2733.

S. A. Messaoudi, M. Pokojovy, B. Said-Houari; Nonlinear damped Timoshenko system with second sound-Global existence and exponential stability, Mathematical Methods in the Applied

Sciences, 32(5) (2009), 505-534.

A. A. Keddi, T. A. Apalara, S. A. Messaoudi; Exponential and polynomial decay in a thermoelastic-Bresse system with second sound, Applied Mathematics and Optimization, 77(2) (2018), 315-341.

C. M. Dafermos; Asymptotic stability in viscoelasticity, Archive for Rational Mechanics and Analysis, 37(4) (1970), 297-308.

V. Pata, E. Vuk; On the exponential stability of linear thermoelasticity, Continuum Mechanics and Thermodynamics, 12(2) (2000), 121-130.

A. Fareh; Exponential stability of a porous thermoelastic system with Gurtin-Pipkin thermal law, Revista de la Real Academia de Ciencias Exactas, F sicas y Naturales. Serie A. Matematicas, 116(1) (2022), 1-19.

F. Dell'Oro, V. Pata; On the stability of Timoshenko systems with Gurtin-Pipkin thermal law, Journal of Di erential Equations, 257(2) (2014), 523-548.

F. Dell'Oro; Asymptotic stability of thermoelastic systems of Bresse type, Journal of Differential Equations, 258(11) (2015), 3902-3927.

B. Said-Houaria, S. A. Messaoudi; Decay property of regularity-loss type of solutions in elastic solids with voids, Applicable Analysis, 92(12) (2013), 2487-2507.

A. Guesmia; Well-posedness and energy decay for Timoshenko systems with discrete time delay under frictional damping and/or in nite memory in the displacement, Afrika Matematika, 28(7-8) (2017), 1253-1284.

A. Pazy; Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York (1983).

Downloads

Published

2023-06-28

Issue

Section

Articles

Categories

How to Cite

Exponential stability for porous thermoelastic systems with Gurtin-Pipkin flux. (2023). Electronic Journal of Differential Equations, 2023(01-87), No. 44, 1-17. https://doi.org/10.58997/ejde.2023.44