Uniqueness of entropy solutions to fractional conservation laws with "fully infinite" speed of propagation

Abstract : 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.
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Submitted on : Monday, July 22, 2019 - 5:42:04 PM
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B Andreianov, M Brassart. Uniqueness of entropy solutions to fractional conservation laws with "fully infinite" speed of propagation. 2019. ⟨hal-02190753⟩

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