THE CAUCHY PROBLEM FOR CONSERVATION LAWS 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

We study the Cauchy problem for multi-dimensional nonlinear conservation laws with multiplicative stochastic perturbation. Using the concept of measure-valued solutions and Kruzhkov's entropy formulation, the existence and uniqueness of an entropy solution is established.

Mots clés: Stochastic PDE; first-order hyperbolic equation; Cauchy problem; multiplicative stochastic perturbation; Young measures; Kruzhkov's entropy

Domaines: Equations aux dérivées partielles [math.AP]

Caroline Bauzet, Guy Vallet, Petra Wittbold. THE CAUCHY PROBLEM FOR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION . Journal of Hyperbolic Differential Equations, 2012, ⟨10.1142/S0219891612500221⟩. ⟨hal-01309552⟩