ITM Web Conf.
Volume 34, 2020International Conference on Applied Mathematics and Numerical Methods – third edition (ICAMNM 2020)
|Number of page(s)||8|
|Published online||03 December 2020|
An approach with Lagrange identity of the mixed problem in theory of strain gradient thermoelasticity
Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania
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In our paper we ﬁrst deﬁne the mixed initial-boundary values problem in the theory of strain gradient thermoelasticity. With the help of an identity of Lagrange’s type, we then prove some theorems regarding the uniqueness of the solution of this mixed problem and also two results regarding the continuous dependence of solutions on initial data and on the charges. We must ouline that we obtain these qualitative results without recourse to any laws of conservation of energy and without recourse to any boundedness assumptions on the coeﬃcients. It is equally important to note that we do not impose restrictions on the elastic coeﬃcients regarding their positive deﬁnition.
Key words: Lagrange’s identity / strain gradient thermoelasticity / uniqueness / continuous dependence results
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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