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.
Entropic Burgers’ equation via a minimizing movement scheme based on the Wasserstein metric / Gigli, Nicola; Otto, Felix. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 47:1-2(2013), pp. 181-206. [10.1007/s00526-012-0515-2]
Entropic Burgers’ equation via a minimizing movement scheme based on the Wasserstein metric
Gigli, Nicola;
2013-01-01
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 (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.| File | Dimensione | Formato | |
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