On a high-dimensional nonlinear stochastic partial differential equation

Lahcen Boulanba (1) , Mohamed Mellouk (2)

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

In this paper we investigate a nonlinear stochastic partial differential equation (spde in short) perturbed by a space-correlated Gaussian noise in arbitrary dimension, 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: Skorohod representation theorem; Stochastic partial differential equations; non-Lipschitz coefficients; martingale problem; Gaussian noises; Skorohod representation theorem.

Domaines: Probabilités [math.PR]

Lahcen Boulanba, Mohamed Mellouk. On a high-dimensional nonlinear stochastic partial differential equation. 2011. ⟨hal-00707241⟩