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.
Author NameAffiliationE-mail
HU Yanbo Department of Mathematics, Hangzhou Normal University,Hangzhou 310036, China; School of Mathematical Sciences, Fudan University,Shanghai 200433, China. yanbo.hu@hotmail.com 
WANG Guodong Department of Mathematics and Physics, Anhui University of Architecture, Hefei 230601, China. yxgdwang@163.com 
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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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