Scalar conservation laws with stochastic forcing

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 sto...

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Bibliographic Details
Published in:Journal of functional analysis 2010, Vol.259 (4), p.1014-1042
Main Authors: Debussche, A., Vovelle, J.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Conservation laws
Entropy solutions
Kinetic formulation
Mathematics
Probability
Stochastic partial differential equations
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Summary: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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2010.02.016