2017/07/03 by Sascha Trostorff, Trostorff, Sascha · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #math.AP #math.FA
paper · pdf · doi:10.48550/arxiv.1707.00429
openalex publication_date 2017/07/03 · arxiv created 2017/07/07 · arxiv updated 2017/07/10 · openalex created_date 2023/03/08 · openalex updated_date 2026/07/28
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.