In this note we study the generation of C_0-semigroups by first order differential operators on L^p(R_+ , C^l) × L^p ([0, 1], C^m) with general boundary conditions. In many cases we are able to characterize the generation property in terms of the invertibility of a matrix associated to the boundary conditions. The abstract results are used to study well-posedness of transport equations on non-compact metric graphs.

Flows on Metric Graphs with General Boundary Conditions

Engel, Klaus-Jochen;
2022

Abstract

In this note we study the generation of C_0-semigroups by first order differential operators on L^p(R_+ , C^l) × L^p ([0, 1], C^m) with general boundary conditions. In many cases we are able to characterize the generation property in terms of the invertibility of a matrix associated to the boundary conditions. The abstract results are used to study well-posedness of transport equations on non-compact metric graphs.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/184332
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