On the Well-posedness of Evolutionary Equations on Infinite Graphs
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 ), we can therefore show well-posedness results for the respective evolutionary problems.
KeywordsEvolutionary equations on graphs (skew-)self-adjoint operators
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