The four thermodynamic potentials, the internal energy u 1⁄4 uð ij; sÞ, the Helmholtz free energy f 1⁄4 f ð ij; T Þ, the Gibbs energy g 1⁄4 gðrij; T Þ and the enthalpy h 1⁄4 hðrij; sÞ are derived, independently of each other, by using the Duhamel–Neumann extension of Hooke’s law and an assumed linear dependence of the specific heat on temperature. A systematic procedure is then presented to exp...

Thermodynamic (Anderson 2005) and elastic properties (Musgrave 1970) of minerals provide the fundamental information needed to analyze seismic observations and to model Earth’s dynamic state. The connection between pressure, temperature, chemical composition, and mineralogy that produce seismic velocity gradients, heterogeneities, and discontinuities, can be established with knowledge of thermo...

Abstract In this work, we investigate a one-dimensional porous-elastic system with thermoelasticity of type III. We establish the well-posedness and stability for cases equal nonequal speeds wave propagation. At end, use some numerical approximations based on finite difference techniques to validate theoretical results.

Abstract In this work, we study a two-dimensional problem involving thermoelastic body with four dissipative mechanisms. The well-known theory proposed by Lord and Shulman is used. existence uniqueness of solution proved using linear semigroups. Then, introducing some assumptions the coupling coefficients, prove that energy decay exponential. An extension to provided Green Lindsay briefly prese...