In this paper, we investigate a model of poro-thermoelasticity with microtemperatures, where the behavior body is influenced by history both temperature and microtemperatures. Mathematically, translates into system partial integro-differential equations. Under suitable condition on tensors appearing in model, prove that resulting well posed. one-dimensional case, exponential decay energy proved.

In the last twenty years, analysis of problems involving dual-phase-lag models has received an increasing attention. this work, we consider coupling between one these and microtemperatures effects. order to overcome infinite speed paradox, two relaxation parameters are introduced for each evolution equation related temperature microtemperatures, leading a system linear hyperbolic partial differ...

This study is concerned with the theory of Cosserat thermoelastic media, whose micro-particles possess microtemperatures. The mixed initial boundary value problem considered in this context transformed a temporally evolutionary equation on Hilbert space. Using some results from semigroups, existence and uniqueness solution proved. In same manner, it approached continuous dependence upon data lo...

In this paper, we propose a system of equations governing the dual-phase-lag heat conduction with microtemperatures. Several conditions on coefficients are imposed so that energy is positive definite and dissipative. On base prove well-posedness exponential stability by means semigroup theory frequency domain method.

A two dimensional deformation due to internal heat source in a thermoelastic solid with microtemperatures under the dependence of modulus of elasticity and thermal conductivity on reference temperature has been studied. A mechanical force of constant magnitude is applied at the free surface of thermoelastic half space. The normal modes technique has been applied to obtain the exact expressions ...