On the well-posedness of evolutionary equations on infinite graphs

Marcus Waurick, Michael Kaliske

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

Abstract

The notion of systems with integration by parts is introduced.With this notion, the spatial operator of the transport equation and the spatial operator of the wave or heat equations on graphs can be defined.Th e graphs, which we consider, can consist of arbitrarily many edges and vertices.The respective adjoints of the operators on those graphs can be calculated and skew-selfadjoint operators can be classified via boundary values.Using the work of R.Picard (Math. Meth.App.Sci.32: 1768–1803 [2009]), we can therefore show well-posedness results for the respective evolutionary problems.
Original languageEnglish
Title of host publicationSpectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations
Subtitle of host publication21st International Workshop on Operator Theory and Applications, Berlin, July 2010
EditorsWolfgang Arendt, Joseph A. Ball, Jussi Behrndt, Karl-Heinz Förster, Volker Mehrmann, Carsten Trunk
Place of PublicationHeidelberg
Pages653-666
Number of pages14
DOIs
Publication statusPublished - 16 Jun 2012

Publication series

NameOperator Theory: Advances and Applications
PublisherSpringer
Volume221

Keywords

  • evolutionary equations
  • (skew)-self-adjoint operators
  • spatial operator

Cite this

Waurick, M., & Kaliske, M. (2012). On the well-posedness of evolutionary equations on infinite graphs. In W. Arendt, J. A. Ball, J. Behrndt, K-H. Förster, V. Mehrmann, & C. Trunk (Eds.), Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations: 21st International Workshop on Operator Theory and Applications, Berlin, July 2010 (pp. 653-666). (Operator Theory: Advances and Applications ; Vol. 221).. https://doi.org/10.1007/978-3-0348-0297-0