On non-autonomous evolutionary problems

Rainer Picard, Sascha Trostorff, Marcus Waurick, Maria Wehowski

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

The paper extends well-posedness results of a previously explored class of time-shift invariant evolutionary problems to the case of non-autonomous media. The Hilbert space setting developed for the time-shift invariant case can be utilized to obtain an elementary approach to non-autonomous equations. The results cover a large class of evolutionary equations, where well-known strategies like evolution families may be difficult to use or fail to work. We exemplify the approach with an application to a Kelvin–Voigt-type model for visco-elastic solids.
Original languageEnglish
Pages (from-to)751-776
Number of pages26
JournalJournal of Evolution Equations
Volume13
Issue number4
Early online date15 Sep 2013
DOIs
Publication statusPublished - 31 Dec 2013

Keywords

  • evolutionary problems
  • non-autonomous equations
  • evolutionary equations
  • Hilbert space

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