Two-parameters semigroups for linear evolution equations

Abstract

We establish sufficient conditions insuring the existence of mild solutions for a class of initial boundary value problem of time homogeneous evolution system of parabolic type defined on a Banach space. A concrete real-world example is provided to illustrate the result. A first application of the obtained results deals with a system of Volterra integro-differential equations. A second one concerns a class of elliptic second order differential equations.