Non-autonomous Evolution Inclusions and Control System

Abstract

In this chapter we consider the topological structure of the solution set of non-autonomous parabolic evolution inclusions with time delay, defined on noncompact intervals. The result restricted to compact intervals is then extended to non-autonomous parabolic control problems with time delay . Moreover, as the applications of the information about the structure, we establish the existence result of global mild solutions for non-autonomous Cauchy problems subject to nonlocal condition , and prove the invariance of a reachability set for non-autonomous control problems under single-valued nonlinear perturbations. Finally, some illustrating examples are supplied.