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An \(L^1\)-theory for scalar conservation laws with multiplicative noise on a periodic domain. (English) Zbl 1394.35262

Summary: We study the Cauchy problem for a multi-dimensional scalar conservation law with a multiplicative noise. Our aim is to give the well-posedness of an \(L^1\)-solution characterized by a kinetic formulation under appropriate assumptions. In particular, we focus on the existence of such a solution.

MSC:

35L04 Initial-boundary value problems for first-order hyperbolic equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35L65 Hyperbolic conservation laws
35R60 PDEs with randomness, stochastic partial differential equations
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References:

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