Exponential Stability and Initial Value Problems for Evolutionary Equations

Exponential Stability and Initial Value Problems for Evolutionary Equations

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 ex...

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Bibliographic Details
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
Description
Summary: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.

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