Entropic Burgers’ equation via a minimizing movement scheme based on the Wasserstein metric

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 (Otto, Commun Pure Appl Math, 1999). In this paper, we give a simpler proof by verifying that the anti-derivative is a viscosity solution of the associated Hamilton Jacobi equation.