On higher index differential-algebraic equations in infinite dimensions

Sascha Trostorff, Marcus Waurick

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

3 Citations (Scopus)
9 Downloads (Pure)

Abstract

We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for arbitrary initial values in a distributional sense. Moreover, we construct a nested sequence of subspaces for initial values in order to obtain classical solutions.
Original languageEnglish
Title of host publicationThe Diversity and Beauty of Applied Operator Theory
EditorsAlbrecht Böttcher, Daniel Potts, Peter Stollmann, David Wenzel
Place of PublicationCham, Switzerland
PublisherSpringer
Pages477-486
Number of pages10
Volume268
ISBN (Print)9783319759951
DOIs
Publication statusPublished - 28 Apr 2018
EventInternational Workshop on Operator Theory and its Applications - Technische Universität Chemnitz, Chemnitz, Germany
Duration: 14 Aug 201718 Aug 2017

Publication series

NameOperator Theory: Advances and Applications
PublisherSpringer
Volume268
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Workshop

WorkshopInternational Workshop on Operator Theory and its Applications
CountryGermany
CityChemnitz
Period14/08/1718/08/17

Keywords

  • differential-algebraic equations
  • higher index
  • infinite-dimensional state space
  • consistent initial values
  • distributional solutions
  • Hilbert space

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