LOCAL $K$-CONVOLUTED $C$-SEMIGROUPS AND ABSTRACT CAUCHY PROBLEMS

Convoluted C-cosine Functions and Convoluted C-semigroups

Evolution Semigroups for Nonautonomous Cauchy Problems

In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP ) { u̇(t) = A(t)u(t) u(s) = x ∈ X on a Banach space X by the existence of certain evolution semigroups. Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions. As a typical example, we discuss the so called “...

Integrated Semigroups and Their Applications to the Abstract Cauchy Problem

This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...

Perturbation Theorems for Convoluted C-semigroups and Cosine Functions

Abstract Cauchy problems and stochastic integral equations

Cauchy problems and stochastic integral equations Bachelor thesis, June 21, 2011 Thesis supervisor: dr. O. van Gaans Mathematisch Instituut, Universiteit Leiden