A Lemma on C0-semigroups and applications

In this note we characterize a large class of C0-semigroups which can be applied to prove the existence and the uniqueness of the solutions of many systems of partial differential equations. In fact, we apply our result to a strongly damped wave equation, damped vibration of a string equation and reaction diffusion systems. Finally, we formulate an open problem. Mathematics Subject Classification (2000): Primary 47D06; Secondary 35K90 Key words: C0-semigroup, systems of partial differential equations, existence of solutions Quaestiones Mathematicae 26(2003), 247–26