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On the backward in time problem for the thermoelasticity with two temperatures
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada
Electronic version of an article published as "Discrete and continuous dynamical series", vol. 19, no 3, May 2014, p. 679-695. DOI 10.3934/dcdsb.2014.19.679.
This paper is devoted to the study of the existence, uniqueness, continuous dependence and spatial behaviour of the solutions for the backward in time problem determined by the Type III with two temperatures thermoelastodynamic theory. We first show the existence, uniqueness and continuous dependence of the solutions. Instability of the solutions for the Type II with two temperatures theory is proved later. For the one-dimensional Type III with two temperatures theory, the exponential instability is also pointed-out. We also analyze the spatial behaviour of the solutions. By means of the exponentially weighted Poincare inequality, we are able to obtain a function that defines a measure on the solutions and, therefore, we obtain the usual exponential type alternative for the solutions of the problem defined in a semi-infinite cylinder.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
Differential equations, Partial
Thermoelasticity--Mathematics
Backward in time problem
Type III with two temperatures thermoelasticity
existence
continuous dependence
spatial growth/decay of solutions
energy arguments
WELL-POSED PROBLEM
ENERGY-DISSIPATION
CONTINUOUS DEPENDENCE
HEAT-CONDUCTION
SPATIAL DECAY
TEMPERATURE THERMOELASTICITY
UNIQUENESS
STABILITY
PROPAGATION
BOUNDARY
Elasticitat
Equacions diferencials parcials
Termoelasticitat
Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application
Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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