Scalar conservation laws with stochastic forcing

Arnaud Debussche (1, 2) , Julien Vovelle (3)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 ICJ - Institut Camille Jordan

We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well-posed: it admits a unique solution, characterized by a kinetic formulation of the problem, which is the limit of the solution of the stochastic parabolic approximation.

Mots clés: Stochastic partial differential equations; conservation laws; kinetic formulation; entropy solutions

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Arnaud Debussche, Julien Vovelle. Scalar conservation laws with stochastic forcing. Journal of Functional Analysis, 2010, 259 (4), pp.1014-1042. ⟨10.1016/j.jfa.2010.02.016⟩. ⟨hal-00451641v2⟩