In this thesis，we prove a classical multiplier theorem introduced by H¨ormander in 1960 and use it in order to give a necessary and su?cient condition for a symmetric hyperbolic system to be well-posed in Lp(Rn，CN )-a result that was shown first by Brenner in 1966. Moreover，we show that hyperbolic equations of second order are well-posed in Lp(Rn) for p=2 if and only if n=1 and apply this result in order to show the ill-posedness of a non-local version of the wave equation. Finally，we study thermoelastic plates in the last section. We establish the well-posedness for the equations with Fourier’s and Cattaneo’s law with and without rotation inertia in suitable L2(Rn)-spaces. Furthermore，we show that the generated semigroups are neither analytic nor bounded except for the case where Fourier’s law is considered without rotation inertia. In addition，we use the ill-posedness of the non-local wave equation in order to derive an ill-posedness result for the thermoelastic plate with rotation inertia in some Lp(Rn)-spaces.