LINEAR TRANSPORT OF PARTICLES ON NETWORKS

We introduce a model of transport of particles in a network, which is represented by a connected graph with m vertices and n edges. Each edg e represents a one-dimensional conductor of particles, whose behavior is described by means of a linear Boltzmann-lilte equation. In graph v ertices, a system of linear boundary conditions is given which takes i nto account the exchanges of particles between the edges. The well-pos edness of the initial value problem is studied into an abstract L(1)-l ike setting and the structure of the solution is given for tile simple st case of pure streaming transport.