2021/09/28 by Marco Pozza, Pozza, Marco, Antonio Siconolfi +1
Engineering · Mathematics · Physics and Astronomy · #35B51 #35F21 #35R02 #49L25 #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Quantum chaos and dynamical systems
paper · doi:10.48550/arxiv.2109.13587
openalex publication_date 2021/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We provide a Lax-Oleinik-type representation formula for solutions of time-dependent Hamilton-Jacobi equations, posed on a network with a rather general geometry, under standard assumptions on the Hamiltonians. It depends on a given initial datum at t=0 and a flux limiter at the vertices, which both have to be assigned in order the problem to be uniquely solved. Previous results in the same direction are solely in the frame of junction, namely network with a single vertex. An important step to get the result is to define a suitable action functional and prove existence as well as Lipschitz-continuity of minimizers between two fixed points of the network in a given time, despite the fact that the integrand lacks convexity at the vertices.