We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential stability for the Lord-Shulman model.

We use the Lagrange identity method and the logarithmic convexity to obtain uniqueness and exponential growth of solutions in the thermoelasticity of type III and thermoelasticity without energy dissipation. As this is not the first contribution of this kind in this theory, it is worth remarking that the assumptions we use here are different from those used in other previous contributions. We a...

Based on Green–Lindsay generalized thermoelasticity theory, this paper presents a new refined higher-order time-derivative model. Thinner one-dimensional skin tissue is considered when its inner surface free of traction and does not show any temperature increase. The tissue’s bounding has been heated by ramp-type heating. classical thermoelastic theories are obtained from the present general fo...

The governing equations of generalized magneto-thermoelasticity with hydrostatic initial stress are solved for surface wave solutions. The particular solutions in the half-space are applied to the boundary conditions at the free surface of the half-space to obtain the frequency equation of Rayleigh wave. The frequency equation is approximated for small thermal coupling and small reduced frequen...

A two-dimensional multi-phase lag model in the context of generalized thermoelasticity is established for an isotropic half-space medium. vector-matrix differential equation obtained from governing equations using normal mode analysis. The eigenvalue approach applied to obtain solutions. temperature-dependent displacements, stresses, strains are calculated numerically and represented graphicall...