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Frid, Hermano; Li, Yachun; Marroquin, Daniel; Nariyoshi, João F. C.; Zeng, Zirong
Stochastic partial differential equations : analysis and computations, 12/2022, Letnik: 10, Številka: 4Journal Article
We establish the well-posedness of the Neumann problem for stochastic conservation laws with multiplicative noise. As a crucial point in order to prove the uniqueness of the kinetic solution to the referred problem we establish a new strong trace theorem for stochastic conservation laws, which extends to the stochastic context the pioneering theorem by Vasseur. Existence of kinetic solutions is proved through the vanishing viscosity method and the detailed analysis of the corresponding stochastic parabolic problem is also made here for the first time, as far as the authors know.
