Well-posedness theory for nonlinear scalar conservation laws on networks
Numerical Analysis
2021-02-15 v1 Numerical Analysis
Abstract
We consider nonlinear scalar conservation laws posed on a network. We establish stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and convergence to the unique entropy solution, thus establishing existence of a solution in the process. Both our existence and stability/uniqueness theory is centred around families of stationary states for the equation. In one important case -- for monotone fluxes with an upwind difference scheme -- we show that the set of (discrete) stationary solutions is indeed sufficiently large to suit our general theory. We demonstrate the method's properties through several numerical experiments.
Keywords
Cite
@article{arxiv.2102.06400,
title = {Well-posedness theory for nonlinear scalar conservation laws on networks},
author = {Ulrik Skre Fjordholm and Markus Musch and Nils Henrik Risebro},
journal= {arXiv preprint arXiv:2102.06400},
year = {2021}
}