Abstract We introduce a kinetic formulation for scalar conservation laws with nonlocal and nonlinear diffusion terms. We deal with merely L1 initial data, general self-adjoint pure jump Lévy operators, and locally Lipschitz nonlinearities of porous medium kind possibly strongly degenerate. The cornerstone of the formulation and the uniqueness proof is an adequate explicit representation of the dissipation measure associated to the diffusion. This measure is a function in our nonlocal framework. Our approach is inspired from the second order theory unlike the cutting technique previously introduced for bounded entropy solutions. The latter technique no longer seems to fit the kinetic setting. This is moreover the first time that the more standard and sharper tools of the second order theory are faithfully adapted to fractional conservation laws.

中文翻译：

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分数守恒定律的非局部耗散测度和 L1 动力学理论

摘要 我们介绍了具有非局部和非线性扩散项的标量守恒定律的动力学公式。我们仅处理 L1 初始数据、一般自伴随纯跳跃 Lévy 算子和多孔介质类型的局部 Lipschitz 非线性可能会强烈退化。公式和唯一性证明的基石是与扩散相关的耗散度量的充分明确表示。这个度量是我们非本地框架中的一个函数。我们的方法受到二阶理论的启发，与之前为有界熵解引入的切割技术不同。后一种技术似乎不再适合动力学设置。此外，这是第一次将二阶理论的更标准和更锐利的工具忠实地适用于分数守恒定律。