we shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by b‎. ‎ya‎. ‎levin in a half plane‎.

Lp–Lq decay estimates of solutions to Cauchy problems of linear thermoelastic systems with second sound in three spatial variables are studied. By carefully analysis of the different effects of higher, middle and lower frequencies in phase space, the asymptotic behaviour of characteristic roots of coefficient matrices is obtained. Then, with the help of the information on characteristic roots a...

A two-dimensional theoretical model for the field generated in the thermoelastic regime by line-focused laser illumination of a homogeneous, isotropic, linearly elastic half-space is presented. The model accounts for the effects of thermal diffusion and optical penetration, as well as the finite width and duration of the laser source. The model is obtained by solving the thermoelastic problem i...

This paper estimated the problem of one-dimensional generalized thermoelastic half-space in medium considering two models: Lord and Shulman (LS) model Dual-Phase-Lag (DPL) model. We assumed that surface was free from traction force under an exponentially varying external heat source at boundary with time. The technique homotopy perturbation has been applied to find approximate solution for inte...

In this paper, the surface waves propagation in a generalized magneto-thermoelastic materials taking (Green Lindsay) model with voids and initial stress is investigated. The basic governing equations have been formulated in xz-plane and the magnetic field is considered in y-axis that acts perpendicular to the wave propagation. Lame's potential method is applied to solve the problem. The boundar...

In work reported at last year’s QNDE meeting, a first step towards the development of a model for the Scanning Laser Source (SLS) technique was presented, which provides an analytical formulation for the transient response of an isotropic, homogeneous, linearly elastic half-space submitted to a pulsed laser line source operating in the thermoelastic regime. The formulation takes into account op...