5 papers
Network transport with nonlinear dynamics at the nodes
Jacek Banasiak, Adam Błoch
In this paper, we consider a network transport model in which agents moving along the edges can contribute to dynamics at nodes or bypass them. The model takes the form of a system…
Existence and explicit formula for a semigroup related to some network problems with unbounded edges
Adam Błoch
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-semigrou…
Telegraph systems on networks and port-Hamiltonians. III. Explicit representation and long-term behaviour
Jacek Banasiak, Adam Błoch
In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary c…
Telegraph type systems on networks and port-Hamiltonians. II. Graph realizability
Jacek Banasiak, Adam Błoch
Hyperbolic systems on networks often can be written as systems of first order equations on an interval, coupled by transmission conditions at the endpoints, also called port-Hamilt…
Telegraph systems on networks and port-Hamiltonians. I. Boundary conditions and well-posedness
Jacek Banasiak, Adam Błoch
The paper is concerned with a system of linear hyperbolic differential equations on a network coupled through general transmission conditions of Kirchhoff's type at the nodes. We d…