Exponential Stability and Initial Value Problems for Evolutionary Equations

• Main Author: Trostorff, Sascha
• Other Authors: Technische Universität Dresden, Fakultät Mathematik und Naturwissenschaften
• Format: Doctoral Thesis
• Language: English
• Published: Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden 2018
• Subjects: Partielle Differentialgleichungen; Wohlgestelltheit; Exponentielle Stabilität; Anfangswerte und Vorgeschichten; Delay Gleichungen; Integro-Differentialgleichungen; partial differential equations; well-posedness; exponential stability; initial values and pre-histories; delay equations; integro-differential equations; ddc:510; rvk:SK 540
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-236494; http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-236494; http://www.qucosa.de/fileadmin/data/qucosa/documents/23649/habil_trostorff.pdf

The thesis deals with so-called evolutionary equations, a class of abstract linear operator equations, which cover a huge class of partial differential equation with and without memory. We provide a unified Hilbert space framework for the well-posedness of such equations. Moreover, we inspect the exponential stability of those problems and construct spaces of admissible inital values and pre-histories, on which a strongly continuous semigroup could be associated with the given problem. The theoretical results are illustrated by several examples.