<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In our study we formulated the mixed initial boundary value problem corresponding to the thermoelasticity of type III for bodies with dipolar structure. In main section we approached four qualitative results regarding the solutions for this problem. In two of these (in the first two theorems) we obtained two results of uniqueness, proved in different ways. Also, we proven two results which show that the solutions of the considered problem depend continuously with respect to the supply terms. We use different procedures in the two theorems on continuous dependence, but we essentially rely on the auxiliary results from Section 3 and Gronwall-type inequalities. It is important to emphasize that all results are obtained by imposing on the basic equations and basic conditions, average constraints that are common in the mechanics of continuous solids.</p></abstract>

In our study we formulated the mixed initial boundary value problem corresponding to the thermoelasticity of type III for bodies with dipolar structure. In main section we approached four qualitative results regarding the solutions for this problem. In two of these (in the first two theorems) we obtained two results of uniqueness, proved in different ways. Also, we proven two results which show that the solutions of the considered problem depend continuously with respect to the supply terms. We use different procedures in the two theorems on continuous dependence, but we essentially rely on the auxiliary results from Section 3 and Gronwall-type inequalities. It is important to emphasize that all results are obtained by imposing on the basic equations and basic conditions, average constraints that are common in the mechanics of continuous solids.

Qualitative results in thermoelasticity of type III for dipolar bodies

Department of Mathematics and Computer Science

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Qualitative results in thermoelasticity of type III for dipolar bodies"}

In our study we formulated the mixed initial boundary value problem corresponding to the thermoelasticity of type III for bodies with dipolar structure. In...

Qualitative results in thermoelasticity of type III for dipolar bodies

Published Online: Apr 13, 2021

Page range: 127 - 142

Received: May 01, 2020

Accepted: Jun 01, 2020

DOI: https://doi.org/10.2478/auom-2021-0009

Keywords
thermoelasticity of type III, dipolar body, uniqueness of solution, Gronwall inequality, continuous dependence

© 2021 M. Marin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Qualitative results in thermoelasticity of type III for dipolar bodies

Published Online: Apr 13, 2021

Page range: 127 - 142

Received: May 01, 2020

Accepted: Jun 01, 2020

DOI: https://doi.org/10.2478/auom-2021-0009

Keywordsthermoelasticity of type III, dipolar body, uniqueness of solution, Gronwall inequality, continuous dependence

© 2021 M. Marin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
thermoelasticity of type III, dipolar body, uniqueness of solution, Gronwall inequality, continuous dependence