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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2022年 / 219卷

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;

引用

页数：13