Global existence and decay properties for solutions of the Cauchy problem in one-dimensional thermoelasticity with second sound

We consider the one-dimensional Cauchy problem in nonlinear thermoelasticity with second sound, where the heat conduction is modeled by Cattaneo's law. After presenting decay estimates for solutions to the linearized problem, including refined estimates for data in weighted Lebesgue-spaces, we prove a global existence theorem for small data together with improved decay estimates, in particular for derivatives of the solutions