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Entropic Burgers’ equation via a minimizing movement scheme based on the Wasserstein metric
Nicola Gigli and Felix OttoAbstract
As noted by the second author in the context of unstable two-phase porous medium flow, entropy solutions of Burgers’ equation can be recovered from a minimizing movement scheme involving the Wasserstein metric in the limit of vanishing time step size [4]. In this paper, we give a simpler proof by verifying that the anti-derivative is a viscosity solution of the associated Hamilton Jacobi equation.
- Received:
- 05.07.12
- Published:
- 06.07.12
- MSC Codes:
- 76S05, 35Q35, 49Q20, 76T99