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Spectral analysis of thermoelastic systems under nonclassical thermal models
- Source :
- Journal of Thermal Stresses. 40:3-24
- Publication Year :
- 2016
- Publisher :
- Informa UK Limited, 2016.
-
Abstract
- We study some spectral properties of the solutions to generalized thermoelastic systems under Lord–Shulman, Green–Lindsay, and Green–Naghdi of type-II models. First, we prove that the linear operator of each model has compact resolvent and generates a C0−semigroup in an appropriate Hilbert space. We also show that there is a sequence of generalized eigenfunctions of the linear operator that forms a Riesz basis. By a detailed spectral analysis, we obtain the expressions of the spectrum and we deduce that the spectrum-determined growth condition holds. Therefore, if the imaginary axis is not an asymptote of the spectrum, we prove that the energy of each model decays exponentially to a rate determined explicitly by the physical parameters. Finally, some simulations are given for each model to support our results.
- Subjects :
- Basis (linear algebra)
010102 general mathematics
Spectrum (functional analysis)
Mathematical analysis
Hilbert space
Eigenfunction
Condensed Matter Physics
01 natural sciences
010101 applied mathematics
Linear map
symbols.namesake
Thermoelastic damping
symbols
General Materials Science
0101 mathematics
Asymptote
Resolvent
Mathematics
Subjects
Details
- ISSN :
- 1521074X and 01495739
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Journal of Thermal Stresses
- Accession number :
- edsair.doi...........c341a14230d6e27786a9de3bdf600df8