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 fixé. Nous nous intéressons ensuite à la limite quand tend vers 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 . In the next step, we investigate the limit as tends to 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{\textendash}Gross{\textendash}Krook} approximation to stochastic scalar conservation laws}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {1500--1528}, publisher = {Gauthier-Villars}, volume = {51}, number = {4}, year = {2015}, doi = {10.1214/14-AIHP610}, mrnumber = {3414456}, zbl = {1329.60214}, language = {en}, url = {http://www.numdam.org/articles/10.1214/14-AIHP610/} }
TY - JOUR AU - Hofmanová, Martina TI - A Bhatnagar–Gross–Krook approximation to stochastic scalar conservation laws JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2015 SP - 1500 EP - 1528 VL - 51 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/14-AIHP610/ DO - 10.1214/14-AIHP610 LA - en ID - AIHPB_2015__51_4_1500_0 ER -
%0 Journal Article %A Hofmanová, Martina %T A Bhatnagar–Gross–Krook approximation to stochastic scalar conservation laws %J Annales de l'I.H.P. Probabilités et statistiques %D 2015 %P 1500-1528 %V 51 %N 4 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/14-AIHP610/ %R 10.1214/14-AIHP610 %G en %F 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/articles/10.1214/14-AIHP610/
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