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On the Well-posedness of Evolutionary Equations on Infinite Graphs

  • Marcus WaurickEmail author
  • Michael Kaliske
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 221)

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.

Keywords

Evolutionary equations on graphs (skew-)self-adjoint operators 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Institut für Statik und Dynamik der TragwerkeTU Dresden Fakultät BauingenieurwesenDresdenGermany

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