Nonlinear well-posedness and rates of decay in thermoelasticity with second sound

摘要

The Cauchy problem in nonlinear thermoelasticity with second sound in one space dimension is considered. Due to Cattaneo's law, replacing Fourier's law for heat conduction, the system is hyperbolic. The local well-posedness as a strictly hyperbolic system is investigated first, and then the relation between energy estimates for non-symmetric hyperbolic systems and well-posedness are discussed. For the global small solution, the long time behavior is described and the decay rates of the L-2-norm are obtained.