Inviscid Burgers as a degenerate elliptic problem
Uditnarayan Kouskiya, Amit Acharya · Quarterly of Applied Mathematics · 2024
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.