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.
"Dispersive mixed-order systems in $L^p$-Sobolev spaces and application to the thermoelastic plate equation." Adv. Differential Equations 24 (7/8) 377 - 406, July/August 2019. https://doi.org/10.57262/ade/1556762453