Accepted at Calc.Var and PDE
Inserted: 9 feb 2010
Last Updated: 2 mar 2012
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. In this paper, we give a simpler proof by verifying that the anti-derivative is a viscosity solution of the associated Hamilton Jacobi equation.
Keywords: Wasserstein distance, viscosity solution, entropy solution, burgers equation