Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions

被引:34
作者
Ambrosio, L
Bouchut, F
De Lellis, C
机构
[1] Max Planck Inst Math Sci, D-04103 Leipzig, Germany
[2] Scuola Normale Super Pisa, Pisa, Italy
[3] ENS, Dept Math & Appl, F-75230 Paris 05, France
关键词
hyperbolic systems; several dimensions; renormalized solutions;
D O I
10.1081/PDE-200040210
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we consider a system of conservation laws in several space dimensions whose nonlinearity is due only to the modulus of the solution. This system, first considered by Keyfitz and Kranzer in one space dimension, has been recently studied by many authors. In particular, using standard methods from DiPerna-Lions theory, we improve the results obtained by the first and third author, showing existence, uniqueness and stability results in the class of functions whose modulus satisfies, in the entropy sense, a suitable scalar conservation law. In the last part of the paper we consider a conjecture on renormalizable solutions and show that this conjecture implies another one recently made by Bressan in connection with the system of Keytitz and Kranzer.
引用
收藏
页码:1635 / 1651
页数:17
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