Global Solvability in Thermoelasticity with Second Sound on the Semi-axis

In this paper, we consider initial boundary value problem for the equations of one-dimensional nonlinear thermoelasticity with second sound in R^+. First, we derive decay rates for linear systems which, in fact, is a hyperbolic systems with a damping term. Then, using this linear decay rates, we get L^1 and L^∞ decay rates for nonlinear systems. Finally, combining with L^2 estimates and a local existence theorem, we prove a global existence and uniqueness theorem for small smooth data.