Staff View: Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect

Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect

In this work, we deal with a one-dimensional Cauchy problem in Timoshenko system with temperature and microtemperature effect. The heat conduction is given by the theory of Lord�Shulman. We prove that the dissipation induced by the coupling of the Timoshenko system with the heat conduction of Lord�S...

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Main Authors:	Choucha A., Saad S.A.A., Jan R., Boulaaras S.
Other Authors:	57216493937
Format:	Article
Published:	Birkhauser 2024
Subjects:	Decay rate Fourier transform Lord�Shulman Mathematical operators Microtemperature damping Partial differential equations Thermoelasticity
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id	my.uniten.dspace-33857
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spelling	my.uniten.dspace-338572024-10-14T11:17:21Z Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect Choucha A. Saad S.A.A. Jan R. Boulaaras S. 57216493937 58342993500 57205596279 36994353700 Decay rate Fourier transform Lord�Shulman Mathematical operators Microtemperature damping Partial differential equations Thermoelasticity In this work, we deal with a one-dimensional Cauchy problem in Timoshenko system with temperature and microtemperature effect. The heat conduction is given by the theory of Lord�Shulman. We prove that the dissipation induced by the coupling of the Timoshenko system with the heat conduction of Lord�Shulman�s theory alone is strong enough to stabilize the system, but with slow decay rate. To show our result, we transform our system into a first order system and, applying the energy method in the Fourier space, we establish some pointwise estimates of the Fourier image of the solution. Using those pointwise estimates, we prove the decay estimates of the solution and show that those decay estimates are very slow, we prove our main result under suitable assumption. � 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG. Final 2024-10-14T03:17:21Z 2024-10-14T03:17:21Z 2023 Article 10.1007/s11868-023-00561-3 2-s2.0-85173652363 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85173652363&doi=10.1007%2fs11868-023-00561-3&partnerID=40&md5=60e1dfd2c9e27936875a1d28123c014e https://irepository.uniten.edu.my/handle/123456789/33857 14 4 65 Birkhauser Scopus
institution	Universiti Tenaga Nasional
building	UNITEN Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Tenaga Nasional
content_source	UNITEN Institutional Repository
url_provider	http://dspace.uniten.edu.my/
topic	Decay rate Fourier transform Lord�Shulman Mathematical operators Microtemperature damping Partial differential equations Thermoelasticity
spellingShingle	Decay rate Fourier transform Lord�Shulman Mathematical operators Microtemperature damping Partial differential equations Thermoelasticity Choucha A. Saad S.A.A. Jan R. Boulaaras S. Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect
description	In this work, we deal with a one-dimensional Cauchy problem in Timoshenko system with temperature and microtemperature effect. The heat conduction is given by the theory of Lord�Shulman. We prove that the dissipation induced by the coupling of the Timoshenko system with the heat conduction of Lord�Shulman�s theory alone is strong enough to stabilize the system, but with slow decay rate. To show our result, we transform our system into a first order system and, applying the energy method in the Fourier space, we establish some pointwise estimates of the Fourier image of the solution. Using those pointwise estimates, we prove the decay estimates of the solution and show that those decay estimates are very slow, we prove our main result under suitable assumption. � 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
author2	57216493937
author_facet	57216493937 Choucha A. Saad S.A.A. Jan R. Boulaaras S.
format	Article
author	Choucha A. Saad S.A.A. Jan R. Boulaaras S.
author_sort	Choucha A.
title	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect
title_short	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect
title_full	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect
title_fullStr	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect
title_full_unstemmed	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect
title_sort	decay rate of the solutions to the cauchy problem of the lord shulman thermoelastic timoshenko model with microtemperature effect
publisher	Birkhauser
publishDate	2024
_version_	1814060047424028672
score	13.222552

Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with microtemperature effect

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