| 胡燕波,王国栋.轴对称压差系统的自相似解[J].数学年刊A辑,2017,38(4):477~486 |
| 轴对称压差系统的自相似解 |
| Self-similar Solutions of the Axisymmetric Pressure-Gradient System |
| Received:July 12, 2014 Revised:July 01, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0039 |
| 中文关键词: Pressure-gradient system, Self-similar solutions, Shock wave |
| 英文关键词:Pressure-gradient system, Self-similar solutions, Shock wave |
| 基金项目:本文受到国家自然科学基金(No.11301128,No.11571088),中国博士后基金(No.2015M580286),
浙江省自然科学基金(No.LY17A010019)和安徽省自然科学基金(No.1508085MA08)的资助. |
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| 中文摘要: |
| 考察了二维压差系统的轴对称活塞均匀膨胀而产生的自相似流动.
在轴对称和自相似假设下, 该问题可以简化为一个自治的非线性常微分方程组的自由边值问题.
通过对常微分方程组的积分曲线性质的详细分析, 建立该自由边值问题正光滑解的整体存在性. |
| 英文摘要: |
| This paper is concerned with self-similar flows of the two-dimensional pressure-gradient system
caused by the uniform expansion of an axially symmetrical piston into the undisturbed fluid.
Under the axisymmetric and self-similar assumptions, the problem can be reduced to a free boundary value
problem of an autonomous nonlinear system of ordinary differential equations. The authors establish the global
existence of the positive smooth solutions to the free boundary value problem by analyzing carefully the
properties of the integral curves of the ODE system. |
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