A Lemma On C₀ -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.

Keywords:

• C0-SEMIGROUP
• SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS
• EXISTENCE OF SOLUTIONS