The Dirichlet problem for a conservation law with a multiplicative stochastic perturbation

Caroline Bauzet (1) , Guy Vallet (1) , Petra Wittbold (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Fakultät für Mathematik der Universität Duisburg-Essen

In this paper, we are interested in the Dirichlet boundary value problem for a multi-dimensional nonlinear conservation law with a multiplicative stochastic perturbation. Using the concept of measure-valued solutions and Kruzhkovʼs semi-entropy formulations, a result of existence and uniqueness of the entropy solution is proved.

Mots clés: Stochastic PDE; First-order hyperbolic equation; Dirichlet problem; Multiplicative stochastic perturbation; Young measures; Kruzhkovʼs semi-entropy

Domaines: Equations aux dérivées partielles [math.AP]

Caroline Bauzet, Guy Vallet, Petra Wittbold. The Dirichlet problem for a conservation law with a multiplicative stochastic perturbation. Journal of Functional Analysis, 2014, ⟨10.1016/j.jfa.2013.06.022⟩. ⟨hal-01309556⟩