Global classical solution for one-dimensional nonlinear thermoelastiticity with second sound on the semi-axis

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 get a uniform a priori estimate. Finally, we use the usual continuation argument to get global solution.