Mathematical problems of thermoelasticity of bodies with microstructure and microtemperatures

The paper deals with the linear theory of thermoelasticity for elastic isotropic microstretch materials with microtemperatures and microdilatations. For the differential equations of pseudo-oscillations the fundamental matrix is constructed explicitly in terms of elementary functions. With the help...

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Bibliographic Details
Published in:Transactions of A. Razmadze Mathematical Institute 2017-12, Vol.171 (3), p.350-378
Main Authors: Giorgashvili, L., Zazashvili, S.
Format: Article
Language:English
Subjects:
Elastic bodies with microstructure
Integral equations
Potential theory
Thermoelasticity with microtemperatures
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Summary:The paper deals with the linear theory of thermoelasticity for elastic isotropic microstretch materials with microtemperatures and microdilatations. For the differential equations of pseudo-oscillations the fundamental matrix is constructed explicitly in terms of elementary functions. With the help of the corresponding Green identities the general integral representation formula of solutions by means of generalized layer and Newtonian potentials are derived. The basic Dirichlet and Neumann type boundary value problems are formulated in appropriate function spaces and the uniqueness theorems are proved. The existence theorems for classical solutions are established by using the potential method.
ISSN:2346-8092
DOI:10.1016/j.trmi.2017.04.002