Time--dependent equations on networks
Analysis of PDEs
2021-06-25 v1
Abstract
We study well posedness of time--dependent Hamilton--Jacobi equations on a network, coupled with a continuous initial datum and a flux limiter. We show existence and uniqueness of solutions as well as stability properties. The novelty of our approach is that comparison results are proved linking the equation to a suitable semidiscrete problem, bypassing doubling variable method. Further, we do not need special test functions, and perform tests relative to the equations on different arcs separately.
Cite
@article{arxiv.2106.12630,
title = {Time--dependent equations on networks},
author = {Antonio Siconolfi},
journal= {arXiv preprint arXiv:2106.12630},
year = {2021}
}