A Lemma On C ₀ -semigroups And Applications

Abstract

In this note we characterize a large class of C ₀-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.