In this paper we study non-smooth solutions of coupled non-stationary problems in thermoelasticity. Since the classical tools based on the Tay-lor's expansion of unknown functions may not be appropriate in obtaining a measure of quality for numerical methods, we apply the averaging Steklov operators and the technique based on the Bramble-Hilbert lemma in order to establish the convergence resul...

In this paper, we will give a global existence theorem in one-dimensional thermoelasticity with second sound in R. For this purpose, we first give the decay rates of the linearized equations with the help of Fourier sine and cosine transformation and the local existence theorem using theorems for quasi-linear symmetric hyperbolic systems. Then we establish some estimates in L, L and L∞ norms to...

First we prove an exponential decay result for solutions of the equations of linear, homogeneous, isotropic thermoelasticity in bounded regions in two or three space dimensions if the rotation of the displacement vanishes. As a consequence, we describe the decay in radially symmetrical situations, and in a cylinder in R3. Then we establish the global existence of solutions to the corresponding ...

The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometerand nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Z...

We study a model for the semiconductor problem that consists of a system of dynamic thermoelasticity equations of displacement and semiconductor equations. This problem arises from the observation that semiconductor devices are too often cracked and broken because of the thermal stresses. Since the heat source generated by Joule heating is quadratic in the gradient of the electrical potential, ...

We consider the Cauchy problem in nonlinear thermoelasticity with second sound in one space dimension. Due to Cattaneo’s law, replacing Fourier’s law for heat conduction, the system is hyperbolic. We first investigate the local well-posedness as a strictly hyperbolic system, and then discuss the relation between energy estimates for non-symmetric hyperbolic systems and well-posedness. For the g...

The term “optical thermoelasticity” is used to describe how the optical properties of a material change when it heated or deformed mechanically. issues effective elastic and heat transfer symmetry are given particular focus. This study gives new nonlocal theoretical formulation for thermo-optical that can be thermomechanical waves plasma relate semiconductor materials such as silicon germanium....

We prove global existence for a simplified model of one-dimensional thermoelasticity. The governing equations satisfy the balance of momentum and a modified energy balance. The application we wish to study by investigating this model are shapememory alloys. They are a prominent example of solids undergoing structural phase transitions. A characteristic feature of these materials is that several...

We consider dynamical and quasi-static thermoelastic contact problems in R modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical and quasi-static nonlinear problems and the exponential stability are investigated using a penalty method. Interior smoothing effects in the quasi-sta...