Calculus of Variations and Geometric Measure Theory
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N. Gigli - F. Otto

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

created by gigli on 09 Feb 2010
modified on 02 Mar 2012


Accepted at Calc.Var and PDE

Inserted: 9 feb 2010
Last Updated: 2 mar 2012

Year: 2010


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


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