Inviscid Burgers as a degenerate elliptic problem
Numerical Analysis
2024-06-21 v6 Numerical Analysis
Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We demonstrate the feasibility of a scheme to obtain approximate weak solutions to the (inviscid) Burgers equation in conservation and Hamilton-Jacobi form, treated as degenerate elliptic problems. We show different variants recover non-unique weak solutions as appropriate, and also specific constructive approaches to recover the corresponding entropy solutions.
Cite
@article{arxiv.2401.08814,
title = {Inviscid Burgers as a degenerate elliptic problem},
author = {Uditnarayan Kouskiya and Amit Acharya},
journal= {arXiv preprint arXiv:2401.08814},
year = {2024}
}