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oai:recercat.cat:2117/3419372026-01-24T11:41:16Zcom_2072_1033col_2072_452950

Uniqueness and exponential instability in a new two-temperature thermoelastic theory Fernández, Jose R. Quintanilla de Latorre, Ramón Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada 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 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) 2021-03-15 Article Fernández, J.; Quintanilla, R. Uniqueness and exponential instability in a new two-temperature thermoelastic theory. "AIMS Mathematics", 15 Març 2021, vol. 6, núm. 6, p. 5440-5451. 2473-6988 https://hdl.handle.net/2117/341937 10.3934/math.2021321 eng 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 12 p. application/pdf AMER INST MATHEMATICAL SCIENCES-AIMS