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Pré-Publication, Document De Travail Année : 2019

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

Résumé

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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Dates et versions

hal-02190753 , version 1 (22-07-2019)
hal-02190753 , version 2 (10-10-2019)
hal-02190753 , version 3 (25-10-2019)

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  • HAL Id : hal-02190753 , version 1

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B Andreianov, M Brassart. Uniqueness of entropy solutions to fractional conservation laws with "fully infinite" speed of propagation. 2019. ⟨hal-02190753v1⟩
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