On the Influence of Viscosity on Riemann Solutions
On the Influence of Viscosity on Riemann Solutions
复制标题
粘度对黎曼解的影响
DOI：
10.1023/a:1022692413112
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发表时间：
1998
影响因子：
1.3
通讯作者：
S. Čanić
中科院分区：
文献类型：
--
作者：
S. Čanić
我们展示了如何黎曼解的存在性和唯一性的影响，用于选择激波承认粘性剖面的粘性的精确形式。我们研究了一个完整的列表余维1分叉，依赖于粘度和区分拉克斯冲击波和不配置文件。这些分支是鞍-鞍异宿分支、同宿分支和非双曲周期轨道分支。我们证明了这些影响Riemann解的存在性和唯一性，并影响组成Riemann解的波的数量和类型。我们提出了“通用”的情况下，粘性黎曼解不同的拉克斯解决方案。
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.