Flows on Metric Graphs with General Boundary Conditions

2021/10/16 by Engel, Klaus-Jochen, Fijavž, Marjeta Kramar · 1 citation
#34G10 #35L04 #35R02 #47D06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2110.08553

Abstract

In this note we study the generation of C₀-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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