  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 inertial term and with Fourier's or Maxwell-Cattaneo's law of heat
conduction.
