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;
2022-01-01
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.File in questo prodotto:
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