A Bhatnagar–Gross–Krook approximation to stochastic scalar conservation laws
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 4, pp. 1500-1528.

Dans ce papier, nous étudions une approximation de type BGK pour des lois de conservations hyperboliques soumises à un bruit multiplicatif. Dans un premier temps, nous utilisons la méthode des caractéristiques dans le cadre stochastique et établissons l’existence d’une solution pour tout paramètre ε fixé. Nous nous intéressons ensuite à la limite quand ε tend vers 0 et prouvons la convergence vers la solution cinétique du problème limite.

We study a BGK-like approximation to hyperbolic conservation laws forced by a multiplicative noise. First, we make use of the stochastic characteristics method and establish the existence of a solution for any fixed parameter ε. In the next step, we investigate the limit as ε tends to 0 and show the convergence to the kinetic solution of the limit problem.

DOI : 10.1214/14-AIHP610
Mots-clés : stochastic conservation laws, kinetic solution, BGK model, hydrodynamic limit, stochastic characteristics method 
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Hofmanová, Martina. A Bhatnagar–Gross–Krook approximation to stochastic scalar conservation laws. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 4, pp. 1500-1528. doi : 10.1214/14-AIHP610. http://www.numdam.org/articles/10.1214/14-AIHP610/

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