The pointwise estimates to solutions for 1-dimensional linear thermoelastic system with second sound

In this paper, we study the thermoelastic system with second sound in one space variable. The mathematical model is a hyperbolic partial differential system with damping term which brings about some parabolic properties. The pointwise estimates of the solution are obtained and from which the generalized Huygens' principle is shown. Our approach is based on detailed analysis on the Green function of the system.