Kinetic solutions for nonlocal stochastic conservation laws. (English) Zbl 1498.60265
Summary: This work is devoted to examining the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator and a multiplicative noise. Our proof for uniqueness is based upon the analysis on double variables method and the existence is enabled by a parabolic approximation.
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 37L55 | Infinite-dimensional random dynamical systems; stochastic equations |
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