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

Nicola Gigli and Felix Otto

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Submission date: 05. Jul. 2012
Pages: 32
published in: Calculus of variations and partial differential equations, 47 (2013) 1-2, p. 181-206 
DOI number (of the published article): 10.1007/s00526-012-0515-2
Bibtex
MSC-Numbers: 76S05, 35Q35, 49Q20, 76T99
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Abstract:
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.