Scalar conservation laws with stochastic forcing |
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| Authors: | A Debussche |
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| Institution: | a IRMAR, ENS Cachan Bretagne, CNRS, UEB. av. Robert Schuman, F-35170 Bruz, France
b Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France |
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| 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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| Keywords: | Stochastic partial differential equations Conservation laws Kinetic formulation Entropy solutions |
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