Weak Solutions of General Systems of Hyperbolic Conservation Laws

被引：0
|
作者：
Tai-Ping Liu
Tong Yang
机构：
[1] Department of Mathematics,
[2] Stanford University,undefined
[3] Stanford,undefined
[4] CA 94305,undefined
[5] USA,undefined
[6] Institute of Mathematics,undefined
[7] Academia Sinica,undefined
[8] Nankang,undefined
[9] Taipei,undefined
[10] Taiwan,undefined
[11] R.O.C.,undefined
[12] Department of Mathematics,undefined
[13] City University of Hong Kong,undefined
[14] Hong Kong,undefined
[15] P.R. China,undefined
来源：
Communications in Mathematical Physics | 2002年 / 230卷
关键词：
Entropy; Weak Solution; Potential Interaction; General System; Characteristic Family;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
 In this paper, we establish the existence theory for general system of hyperbolic conservation laws and obtain the uniform L1 boundness for the solutions. The existence theory generalizes the classical Glimm theory for systems, for which each characteristic field is either genuinely nonlinear or linearly degenerate in the sense of Lax. We construct the solutions by the Glimm scheme through the wave tracing method. One of the key elements is a new way of measuring the potential interaction of the waves of the same characteristic family involving the angle between waves. A new analysis is introduced to verify the consistency of the wave tracing procedure. The entropy functional is used to study the L1 boundedness.
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页码：289 / 327
页数：38
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