Existence and explicit formula for a semigroup related to some network problems with unbounded edges

In this paper we consider an initial-boundary value problem related to some network dynamics where the underlying graph has unbounded edges. We show that there exists a C0-semigroup for this problem using a general result from the literature. We also find an explicit formula for this semigroup. This is achieved using the method of characteristics and then showing that the Laplace transform of the solution is equal to the resolvent operator of the generator.