A Bhatnagar–Gross–Krook approximation to stochastic scalar conservation laws

Hofmanová, Martina

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 $\epsilon$ fixé. Nous nous intéressons ensuite à la limite quand $\epsilon$ 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 $\epsilon$. In the next step, we investigate the limit as $\epsilon$ tends to $0$ and show the convergence to the kinetic solution of the limit problem.

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