Abstract
In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity. The inverse Laplace transforms are computed numerically, and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.