Abstract
In this note we study the generation of C0-semigroups by first order differential operators on Lp(R+,Cℓ)×Lp([0,1],Cm) 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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