Inviscid Burgers as a degenerate elliptic problem

2024/01/16 by Uditnarayan Kouskiya, Amit Acharya, Kouskiya, Uditnarayan +1 · 4 citations
Psychology · Economics, Econometrics and Finance · Engineering · #Optimism, Hope, and Well-being #Stochastic processes and financial applications #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.2401.08814

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.

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