On a high-dimensional nonlinear stochastic partial differential equation

Mohamed Mellouk (1) , Lahcen Boulanba (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 Faculté des Sciences Semlalia [Marrakech]

In this paper we investigate a nonlinear stochastic partial differential equation perturbed by a space-correlated Gaussian noise in arbitrary dimension d>1, with a non-Lipschitz coefficient noisy term. The equation studied coincides in one dimension with the stochastic Burgers equation. Existence of a weak solution is established through an approximation procedure.

Mots clés: stochastic partial differential equations; non-Lipschitz coefficients; martingale problem; Gaussian noises; Skorohod representation theorem

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Mohamed Mellouk, Lahcen Boulanba. On a high-dimensional nonlinear stochastic partial differential equation. Stochastics and Stochastics Reports, 2014, Stochastics 86 (2014), no. 6, (no. 6,), ⟨10.1080/17442508.2014.895496⟩. ⟨hal-01437948⟩