On the well-posedness of evolutionary equations on infinite graphs

Marcus Waurick; Michael Kaliske

doi:10.1007/978-3-0348-0297-0

On the well-posedness of evolutionary equations on infinite graphs

Marcus Waurick, Michael Kaliske

Mathematics And Statistics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

6 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 language	English
Title of host publication	Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations
Subtitle of host publication	21st International Workshop on Operator Theory and Applications, Berlin, July 2010
Editors	Wolfgang Arendt, Joseph A. Ball, Jussi Behrndt, Karl-Heinz Förster, Volker Mehrmann, Carsten Trunk
Place of Publication	Heidelberg
Pages	653-666
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-0348-0297-0
Publication status	Published - 16 Jun 2012

Publication series

Name	Operator Theory: Advances and Applications
Publisher	Springer
Volume	221

Keywords

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

Access to Document

10.1007/978-3-0348-0297-0

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

Waurick, Marcus ; Kaliske, Michael. / On the well-posedness of evolutionary equations on infinite graphs. Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations: 21st International Workshop on Operator Theory and Applications, Berlin, July 2010. editor / Wolfgang Arendt ; Joseph A. Ball ; Jussi Behrndt ; Karl-Heinz Förster ; Volker Mehrmann ; Carsten Trunk. Heidelberg, 2012. pp. 653-666 (Operator Theory: Advances and Applications ).

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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.",

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Waurick, M & Kaliske, M 2012, On the well-posedness of evolutionary equations on infinite graphs. in W Arendt, JA 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. Operator Theory: Advances and Applications , vol. 221, Heidelberg, pp. 653-666. https://doi.org/10.1007/978-3-0348-0297-0

On the well-posedness of evolutionary equations on infinite graphs. / Waurick, Marcus; Kaliske, Michael.
Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations: 21st International Workshop on Operator Theory and Applications, Berlin, July 2010. ed. / Wolfgang Arendt; Joseph A. Ball; Jussi Behrndt; Karl-Heinz Förster; Volker Mehrmann; Carsten Trunk. Heidelberg, 2012. p. 653-666 (Operator Theory: Advances and Applications ; Vol. 221).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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AU - Kaliske, Michael

PY - 2012/6/16

Y1 - 2012/6/16

N2 - 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.

AB - 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.

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KW - (skew)-self-adjoint operators

KW - spatial operator

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DO - 10.1007/978-3-0348-0297-0

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SP - 653

EP - 666

BT - Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

A2 - Arendt, Wolfgang

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A2 - Förster, Karl-Heinz

A2 - Mehrmann, Volker

A2 - Trunk, Carsten

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Waurick M, Kaliske M. On the well-posedness of evolutionary equations on infinite graphs. In Arendt W, Ball JA, Behrndt J, Förster KH, Mehrmann V, Trunk C, editors, Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations: 21st International Workshop on Operator Theory and Applications, Berlin, July 2010. Heidelberg. 2012. p. 653-666. (Operator Theory: Advances and Applications ). doi: 10.1007/978-3-0348-0297-0

On the well-posedness of evolutionary equations on infinite graphs

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