Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada
2021-03-15
IIn this work we consider the temperature-rate dependent two temperatures thermoelastic theory. It has been proposed very recently. We study the case in which the elasticity tensor may not be positive definite. Thus, the problem can be ill posed in the sense of Hadamard. We adapt the logarithmic convexity argument to the specific situation proposed by this theory. That is, we define a suitable function on the solutions satisfying that the logarithm is convex. Uniqueness and instability of the solutions under suitable conditions on the constitutive tensors are proved
Peer Reviewed
Postprint (published version)
Article
English
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències; Thermoelasticity; Temperature-rate dependent two-temperature thermoelasticity: Uniqueness; Logarithmic convexity; Exponential instability; Termoelasticitat; Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application; Classificació AMS::74 Mechanics of deformable solids::74H Dynamical problems; Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer; Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects
AMER INST MATHEMATICAL SCIENCES-AIMS
http://www.aimspress.com/article/doi/10.3934/math.2021321
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105118GB-I00/ES/ANALISIS MATEMATICO APLICADO A LA TERMOMECANICA/
https://creativecommons.org/licenses/by/4.0/
Open Access
Attribution 4.0 International
E-prints [72996]
