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.

中文翻译：

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非局部随机守恒律的动力学解

这项工作致力于检查涉及非局部超临界扩散算子和乘性噪声的一类标量守恒定律的动力学解的唯一性和存在性。我们对唯一性的证明是基于对双变量方法的分析，并且通过抛物线近似来实现存在性。