THE CAUCHY PROBLEM FOR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION

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Stochastic non-isotropic degenerate parabolic–hyperbolic equations (2016, result): “[4] C. Bauzet, G. Vallet, and P. Wittbold.”
Long‐Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws (2014, background): “For stochastic scalar conservation laws driven by additive noise, also including boundary value problems, we refer to the works by E, Khanin, Mazel and Sinai [22], Kim [37], Nakazawa [45], Saussereau and Stoica [51] and Vallet and Wittbold [53] and the references therein.”
Degenerate parabolic stochastic partial differential equations: Quasilinear case (2013, background): “Also in the stochastic setting there are several papers concerned with entropy solutions for hyperbolic conservation laws, the first one being [16] then [2, 10, 27].”
A priori estimates for rough PDEs with application to rough conservation laws (2016, background): “For the sake of a cleaner presentation and to convey as effectively as possible the key points of our strategy we will limit here to discuss the first non–trivial case (namely p ∈ [2, 3)) which shows already the general pattern.”
The Dirichlet problem for a conservation law with a multiplicative stochastic perturbation (2014, methodology): “[4] proved a result of existence and uniqueness of the solution to the multi-dimensional Cauchy problem.”