Co−Semigroups of Contradiction on Banach Spaces and Applications

Abstract

Let X be a Banach space and A : D(A) ⊂ X −→ X be an unbounded linear operator on X. We study the concept of C0−semigroup of contraction on arbitrary Banach space X and give the two characterizations of A called infinitesimal generator of C0−semigroup on X namely, Hille-Yosida and Lumer Phillips characterizations. In the later part, we apply the approach of C0−semigroups to some partial differential equations with boundary conditions.