Dispersive mixed-order systems in L^p-Sobolev spaces and application to the thermoelastic plate equation

Abstract

We study dispersive mixed-order systems of pseudodifferential operators in the setting of Lp-Sobolev spaces. Under the weak condition of quasi-hyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of Lp-Sobolev spaces, a strongly continuous semigroup is in many cases only generated if p=2 or n=1. The results are applied to the linear thermoelastic plate equation inertial term and with Fourier's or Maxwell-Cattaneo's law of heat conduction.