Title: Hamilton–Jacobi problems on graphs and networks.
Abstract: The talk presents some Hamilton–Jacobi problems on networks. The pecu- liarity is that the Hamiltonians on different arcs are unrelated, without any compatibility condition at the vertices. Nevertheless, uniqueness result and comparison principles can be obtained, suitably exploiting the geometry of the network,
Our approach consists in associating to the problem on the network a discrete or semidis- crete equation posed on an underlying abstract graph. This allows testing separately the equations on any arc and proving comparison results without using the doubling variable technique. This is beneficial in the numerical approximation as well.