Vol. 5, No. 2, 2017

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ISSN: 2325-3444 (e-only)
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On the well-posedness of the Green–Lindsay model

Gia Avalishvili, Mariam Avalishvili and Wolfgang H. Müller

Vol. 5 (2017), No. 2, 115–125
DOI: 10.2140/memocs.2017.5.115
Abstract

The present paper is devoted to an investigation of a nonclassical model for inhomogeneous anisotropic thermoelastic bodies with two constant relaxation times originally presented by Green and Lindsay. A variational formulation of the initial-boundary value problem corresponding to the linear dynamical three-dimensional Green–Lindsay model is applied. The corresponding spaces of vector-valued distributions with respect to the time variable with values in Sobolev spaces are defined and the existence and uniqueness of the solution in these spaces as well as continuous dependence of the solution on the given data is shown.

Keywords
nonclassical thermoelasticity, initial-boundary value problem, existence and uniqueness of solution
Mathematical Subject Classification 2010
Primary: 74F05, 74H20, 74H25
Milestones
Received: 5 September 2016
Revised: 12 November 2016
Accepted: 19 December 2016
Published: 13 April 2017

Communicated by Francesco dell'Isola
Authors
Gia Avalishvili
Faculty of Exact and Natural Sciences
I. Javakhishvili Tbilisi State University
3, I. Tchavtchavadze Ave.
0179 Tbilisi
Georgia
Mariam Avalishvili
School of Informatics, Engineering and Mathematics
University of Georgia
77a, M. Kostava Str.
0175 Tbilisi
Georgia
Wolfgang H. Müller
Institute of Mechanics, LKM
Technische Universität Berlin
Einsteinufer 5
D-10587 Berlin
Germany