Flows on metric graphs with general boundary conditions
In this article the authors study the generation of \(\text{C}_0\)-semigroups by first order differential operators on \(\operatorname{L}^p(\mathbb{R}_+,\mathbb{C}^\ell)\times\operatorname{L}^p([0,1],\mathbb{C}^m)\) with general boundary conditions. The authors first characterize the generation property in terms of the invertibility of a matrix associated to the boundary conditions under certain technical conditions on the coefficients of the differential operator. Then they employ their abstract results to study well-posedness of transport equations on non-compact metric graphs. This includes in particular graphs with infinitely many edges or with edges that represent semi-axes.
scientific article; zbMATH DE number 7516724
scientific article