Our goal is to study the uniqueness of bounded entropy solutions for a multidimensional conservation law including a non-Lipschitz convection term and a diffusion term of nonlocal porous medium type. The nonlocality is given by a fractional power of the Laplace operator. For a wide class of nonlinearities, the L 1-contraction principle is established, despite the fact that the "finite-infinite" speed of propagation [Alibaud, JEE 2007] cannot be exploited in our framework; existence is deduced with perturbation arguments. The method of proof, adapted from [Andreianov, Maliki, NoDEA 2010], requires a careful analysis of the action of the fractional laplacian on truncations of radial powers.

中文翻译：

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具有“完全无限”传播速度的分数守恒定律的熵解的唯一性

我们的目标是研究多维守恒定律的有界熵解的唯一性，包括非 Lipschitz 对流项和非局部多孔介质类型的扩散项。非局域性由拉普拉斯算子的分数幂给出。尽管在我们的框架中无法利用“有限-无限”传播速度 [Alibaud, JEE 2007]，但对于一大类非线性，L 1-收缩原理已经成立；存在是用扰动参数推导出来的。取自 [Andreianov, Maliki, NoDEA 2010] 的证明方法需要仔细分析分数拉普拉斯算子对径向幂截断的作用。