DISPERSIVE MIXED-ORDER SYSTEMS IN Lp-SOBOLEV SPACES AND APPLICATION TO THE THERMOELASTIC PLATE EQUATION

We study dispersive mixed-order systems of pseudodifferential operators in the setting of L-p-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 L-p-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 with and without inertial term and with Fourier's or Maxwell-Cattaneo's law of heat conduction.