Semigroups on Product Spaces with Application to Initial Value Problems with Non-Local Boundary Conditions

Abstract

Interest has recently been shown in conditions that a linear operator generates a C0 semigroup on a product space. Such semigroups arise in the study of initial value problems with nonlocal boundary conditions as well as linear functional differential equations. Introduction of semigroups on product spaces also permits study of a wide class of distributed systems with boundary input by means of evolution equations with bounded input operators. New conditions are given which permit unbounded coupling terms in the infinitesimal generator. Their application is examined in a number of examples.