Some remarks on growth and uniqueness in thermoelasticity
type: Item
instance of: scholarly article
title: Some remarks on growth and uniqueness in thermoelasticity
zbMATH Open document ID: 1045.35100
DOI: 10.1155/S0161171203108319
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/50910
review text: Summary: We use the Lagrange identity method and the logarithmic convexity to obtain uniqueness and exponential growth of solutions in the thermoelasticity of type III and thermoelasticity without energy dissipation. As this is not the first contribution of this kind in this theory, it is worth remarking that the assumptions we use here are different from those used in other previous contributions. We assume that the elasticity tensor is positive semidefinite, but we allow that the constitutive tensor of the entropy flux vector \((k_ij)\), which is a characteristic tensor in this theory, is not sign-definite. The Lagrange identity method is used to obtain uniqueness in the context of the thermoelasticity of type III. The fundamental key to obtain exponential growth in the thermoelasticity without energy dissipation is the use of a new functional. This functional is inspired in that it is used when the elasticity tensor is not sign-definite, but \((k_ij)\) is positive definite.
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74H25
zbMATH DE Number: 1883692
author: Ramón Quintanilla
MaRDI profile type: Publication
OpenAlex ID: W2147525581
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description: scientific article; zbMATH DE number 1883692