Some results in Moore‐Gibson‐Thompson thermoelasticity of dipolar bodies
Top Cited Papers
- 14 July 2020
- journal article
- research article
- Published by Wiley in ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
- Vol. 100 (12) , e202000090
Abstract
We consider the mixed initial‐boundary value problem in the context of the Moore‐Gibson‐Thompson theory of thermoelasticity for dipolar bodies. We consider the case of heat conduction with dissipation. Even if the elasticity tensors are not supposed to be positively defined, we have proven both, the uniqueness and the instability of the solution of the mixed problem. In the case that the mass density and the thermal conductivity tensor are positive, we obtain the uniqueness of the solution using some Lagrange type identities.Keywords
This publication has 25 references indexed in Scilit:
- An abstract semigroup approach to the third-order Moore–Gibson–Thompson partial differential equation arising in high-intensity ultrasound: structural decomposition, spectral analysis, exponential stabilityMathematical Methods in the Applied Sciences, 2012
- Thin-walled Structures Made of Foams2010
- Some Estimates on Vibrations in Thermoelasticity of Dipolar BodiesJournal of Vibration and Control, 2009
- Uniqueness and Growth of Solutions in Two-Temperature Generalized Thermoelastic TheoriesMathematics and Mechanics of Solids, 2008
- On A Thermoelastic Three-Phase-Lag ModelJournal of Thermal Stresses, 2007
- Thermal stresses in microstretch elastic platesInternational Journal of Engineering Science, 2005
- The Lagrange identity method in thermoelasticity of bodies with microstructureInternational Journal of Engineering Science, 1994
- Compressible-Fluid DynamicsJournal of Applied Mechanics, 1972
- Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamicsArchive for Rational Mechanics and Analysis, 1971
- Micro-structure in linear elasticityArchive for Rational Mechanics and Analysis, 1964