Global existence and decay of solutions of the Cauchy problem in thermoelasticity with second sound

Abstract

We consider the one-dimensional Cauchy problem in non-linear thermoelasticity with second sound, where the heat conduction is modelled 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.

Keywords:

• thermoelasticity
• decay rate
• Lyapunov functional
• second sound

AMS Subject Classifications:

• 37L15
• 35B35
• 35B37