On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure

We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely...

Full description

Bibliographic Details
Main Authors:	M. Marin, S. Vlase, R. Ellahi, M.M. Bhatti
Format:	Article
Language:	English
Published:	MDPI AG 2019-07-01
Series:	Symmetry
Subjects:	backward in time problem dipolar thermoelastic body uniqueness of solution Cesaro means partition of energies
Online Access:	https://www.mdpi.com/2073-8994/11/7/863

id	doaj-6b56048f191d4b6aa49016e83f1e6f20
record_format	Article
spelling	doaj-6b56048f191d4b6aa49016e83f1e6f202020-11-24T21:30:44ZengMDPI AGSymmetry2073-89942019-07-0111786310.3390/sym11070863sym11070863On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar StructureM. Marin0S. Vlase1R. Ellahi2M.M. Bhatti3Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, RomaniaDepartment of Mechanical Engineering, Transilvania University of Brasov, 500093 Brasov, RomaniaCenter for Modeling & Computer Simulation, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi ArabiaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaWe first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem.https://www.mdpi.com/2073-8994/11/7/863backward in time problemdipolar thermoelastic bodyuniqueness of solutionCesaro meanspartition of energies
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	M. Marin S. Vlase R. Ellahi M.M. Bhatti
spellingShingle	M. Marin S. Vlase R. Ellahi M.M. Bhatti On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure Symmetry backward in time problem dipolar thermoelastic body uniqueness of solution Cesaro means partition of energies
author_facet	M. Marin S. Vlase R. Ellahi M.M. Bhatti
author_sort	M. Marin
title	On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure
title_short	On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure
title_full	On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure
title_fullStr	On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure
title_full_unstemmed	On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure
title_sort	on the partition of energies for the backward in time problem of thermoelastic materials with a dipolar structure
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2019-07-01
description	We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem.
topic	backward in time problem dipolar thermoelastic body uniqueness of solution Cesaro means partition of energies
url	https://www.mdpi.com/2073-8994/11/7/863
work_keys_str_mv	AT mmarin onthepartitionofenergiesforthebackwardintimeproblemofthermoelasticmaterialswithadipolarstructure AT svlase onthepartitionofenergiesforthebackwardintimeproblemofthermoelasticmaterialswithadipolarstructure AT rellahi onthepartitionofenergiesforthebackwardintimeproblemofthermoelasticmaterialswithadipolarstructure AT mmbhatti onthepartitionofenergiesforthebackwardintimeproblemofthermoelasticmaterialswithadipolarstructure
_version_	1725961946912522240

On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure

Similar Items