On the influence of viscosity on Riemann solutions

被引：0
作者：
Čanić S. [1 ]
机构：
[1] Department of Mathematics, Iowa State University, Ames
来源：
Journal of Dynamics and Differential Equations | 1998年 / 10卷 / 1期
基金：
美国国家科学基金会;
关键词：
Conservation laws; Riemann problems; Viscous profile;
D O I：
10.1023/A:1022692413112
中图分类号：
学科分类号：
摘要：
We show how the existence and uniqueness of Riemann solutions are affected by the precise form of viscosity which is used to select shock waves admitting a viscous profile. We study a complete list of codimension-1 bifurcations that depend on viscosity and distinguish between Lax shock waves with and without a profile. These bifurcations are the saddle-saddle heteroclinic bifurcation, the homoclinic bifurcation, and the nonhyperbolic periodic orbit bifurcation. We prove that these influence the existence and uniqueness of Riemann solutions and affect the number and type of waves comprising a Riemann solution. We present "generic" situations in which viscous Riemann solutions differ from Lax solutions. © 1998 Plenum Publishing Corporation.
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页码：109 / 149
页数：40
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