Exponential Stability and Initial Value Problems for Evolutionary Equations

Abstract

In this thesis we consider so-called linear evolutionary problems, a class of linear partial differential equations covering classical elliptic, parabolic and hyperbolic equations from mathematical physics as well as classes of integro-differenital equations, fractional differential equations and delay equations. We address the well-posedness of the problems in a pure Hilbert space setting. Moreover, the exponential stability and the regularity of the problems are studied. In particular, a Hille-Yosida type result is proved, to obtain a strongly continuous semigroup on a suitable state space consisting of admissible initial values and pre-histories. The results are illustrated by various examples.