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On uniqueness and stability for a thermoelastic theory
- Source :
- UPCommons. Portal del coneixement obert de la UPC, Universitat Politècnica de Catalunya (UPC), Recercat. Dipósit de la Recerca de Catalunya, instname
- Publication Year :
- 2017
-
Abstract
- In this paper we investigate a thermoelastic theory obtained from the Taylor approximation for the heat flux vector proposed by Choudhuri. This new thermoelastic theory gives rise to interesting mathematical questions. We here prove a uniqueness theorem and instability of solutions under the relaxed assumption that the elasticity tensor can be negative. Later we consider the one-dimensional and homogeneous case and we prove the existence of solutions. We finish the paper by proving the slow decay of the solutions. That means that the solutions do not decay in a uniform exponential way. This last result is relevant if it is compared with other thermoelastic theories where the decay of solutions for the one-dimensional case is of exponential way.
- Subjects :
- Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials [Àrees temàtiques de la UPC]
General Mathematics
Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC]
Existence
80 Classical thermodynamics, heat transfer [Classificació AMS]
02 engineering and technology
01 natural sciences
Stability (probability)
Instability
symbols.namesake
Thermoelastic damping
0203 mechanical engineering
Taylor series
General Materials Science
Slow decay
Uniqueness
0101 mathematics
Thermoelasticity
Mathematics
Mathematical analysis
Differential equations, Partial
Equacions diferencials parcials
Exponential function
010101 applied mathematics
020303 mechanical engineering & transports
Uniqueness theorem for Poisson's equation
Heat flux
Mechanics of Materials
symbols
Thermoelastodynamics
35 Partial differential equations [Classificació AMS]
Termoelasticitat
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- UPCommons. Portal del coneixement obert de la UPC, Universitat Politècnica de Catalunya (UPC), Recercat. Dipósit de la Recerca de Catalunya, instname
- Accession number :
- edsair.doi.dedup.....20fab3e182faec3b5c2c080c9eeed774