Qualitative Results in the Theory of Thermoelastic Diffusion Mixtures

Abstract

The general equations of motion and constitutive equations are derived in a mixture of two interacting continua, taking into account the effects of heat and diffusion. First, the basic equations of the nonlinear theory of heat and diffusion conducting elastic mixtures are derived in lagrangian description. A frame independent nonlinear constitutive relation is derived. Then, the theory is linearized and field equations are given for both anisotropic and isotropic solids. The continuous dependence of solutions on initial data and body sources, and a uniqueness result are presented. An exponential decay estimate of the solutions is established. Finally, we prove the impossibility of the localization in time of the solutions.

Análise Numérica para Um Problema de Difusão Termoelástica em Domínios Não-Cilíndricos

“…A existência e unicidade do problemaé conhecido na literatura através dos trabalhos de M. Aouadi (ver [1][2][3][4]). Rincon et al [5] analisaram o aspecto numérico do problema termoelástico em domínios não-cilíndricos.…”

A study of influence of diffusion inside a spherical shell under thermoelastic diffusion with relaxation times

“…Singh [17,18] studied the reflection phenomena of waves from the free surface of an elastic solid under theory of generalized thermodiffusion. Aouadi [19][20][21][22][23][24] reported some studies on thermoelastic diffusion and generalized thermoelastic diffusion. Subsequently, great attention has been paid to the theory of thermoelastic diffusion to investigate the nature of mutual interactions of mass diffusion with the temperature and strain fields, and it has been realized that the process of thermodiffusion could have a very considerable influence upon the deformation of the body (see Sharma [25], Sharma et al [26][27][28], Kumar and Kansal [29,30], Ram et al [31], Deswal and Choudhary [32][33][34], Elhagary [35] and Rong-hou et al [36]).…”