A Bhatnagar–Gross–Krook approximation to stochastic scalar conservation laws
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 4, p. 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.
@article{AIHPB_2015__51_4_1500_0,
     author = {Hofmanov\'a, Martina},
     title = {A Bhatnagar--Gross--Krook approximation to stochastic scalar conservation laws},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {4},
     year = {2015},
     pages = {1500-1528},
     doi = {10.1214/14-AIHP610},
     mrnumber = {3414456},
     language = {en},
     url = {http://http://www.numdam.org/item/AIHPB_2015__51_4_1500_0}
}
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/item/AIHPB_2015__51_4_1500_0/

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