Generalized characteristics for finite entropy solutions of Burgers' equation

被引:1
|
作者
Hip, Andres A. Contreras [1 ]
Lamy, Xavier [2 ]
Marconi, Elio [3 ]
机构
[1] Univ Chicago, Dept Math, Chicago, IL USA
[2] Univ Toulouse, Inst Math Toulouse, UMR 5219, CNRS,UPS,IMT, F-31062 Toulouse 9, France
[3] EPFL B, Stn 8, CH-1015 Lausanne, Switzerland
关键词
Generalized characteristics; Finite entropy solutions; Burgers' equation; Lagrangian representation; L 2 stability of shocks; PIECEWISE-SMOOTH SOLUTIONS; STABILITY; UNIQUENESS;
D O I
10.1016/j.na.2022.112804
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove the existence of generalized characteristics for weak, not necessarily entropic, solutions of Burgers' equation & nbsp;& part;(t)u+& part;(x)u(2)/2=0,& nbsp;whose entropy productions are signed measures. Such solutions arise in connection with large deviation principles for the hydrodynamic limit of interacting particle systems. The present work allows to remove a technical trace assumption in a recent result by the two first authors about the L-2 stability of entropic shocks among such non-entropic solutions. The proof relies on the Lagrangian representation of a solution's hypograph, recently constructed by the third author. In particular, we prove a decomposition formula for the entropy flux across a given hypersurface, which is valid for general multidimensional scalar conservation laws. (C)& nbsp;2022 The Author(s). Published by Elsevier Ltd.& nbsp;
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页数:13
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