Uniqueness of entropy solutions to fractional conservation laws with 'fully infinite' speed of propagation
| Autor: | Boris Andreianov, Matthieu Brassart |
|---|---|
| Přispěvatelé: | Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Andreianov, Boris |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Convection
Differential inequalities Radial powers [MATH] Mathematics [math] [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] 01 natural sciences Quantum nonlocality Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Uniqueness [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Entropy formulation [MATH]Mathematics [math] Entropy (arrow of time) L 1 -contraction principle Mathematics Conservation law Applied Mathematics 010102 general mathematics Kato inequality [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA] Fractional laplacian 010101 applied mathematics Nonlocal conservation law Bounded function Porous medium Laplace operator Analysis |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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