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Scalar conservation laws with stochastic forcing

Arnaud Debussche 1, 2 Julien Vovelle 3
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : 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.
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Arnaud Debussche, Julien Vovelle. Scalar conservation laws with stochastic forcing. Journal of Functional Analysis, Elsevier, 2010, 259 (4), pp.1014-1042. ⟨10.1016/j.jfa.2010.02.016⟩. ⟨hal-00451641v2⟩

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