A Bhatnagar–Gross–Krook approximation to stochastic scalar conservation laws
Hofmanová, Martina
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015), p. 1500-1528 / Harvested from Numdam
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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.

Publié le : 2015-01-01
DOI : https://doi.org/10.1214/14-AIHP610 
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     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},
     volume = {51},
     year = {2015},
     pages = {1500-1528},
     doi = {10.1214/14-AIHP610},
     mrnumber = {3414456},
     language = {en},
     url = {http://dml.mathdoc.fr/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) pp. 1500-1528. doi : 10.1214/14-AIHP610. http://gdmltest.u-ga.fr/item/AIHPB_2015__51_4_1500_0/

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