拟线性可化约的双曲型方程组的奇性分析

数学季刊 ›› 2005, Vol. 20 ›› Issue (1): 10-20.

拟线性可化约的双曲型方程组的奇性分析

College of Mathematics and Information Science , Shandong Institute of Business and Technology, Yantai 264005, China

收稿日期:2003-07-01 出版日期:2005-03-30 发布日期:2024-01-25
作者简介:WANG Li-zhen(1976-),female,native of Weifang,Shangdong,candidate for Master degree of Shanghai Jiaotong University,engages in partial differential equation.
基金资助:
Supported by the NSFC(1001024)；

Analysis of Singularity for Reducible Quasi-linear Hyperbolic Systems

College of Mathematics and Information Science , Shandong Institute of Business and Technology, Yantai 264005, China

Received:2003-07-01 Online:2005-03-30 Published:2024-01-25
About author:WANG Li-zhen(1976-),female,native of Weifang,Shangdong,candidate for Master degree of Shanghai Jiaotong University,engages in partial differential equation.
Supported by:
Supported by the NSFC(1001024)；

摘要/Abstract

摘要： In this paper we investigate the formation of singularities of hyperbolic systems. Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.

关键词: quasi-linear , systems;strictly , hyperbolic , systems;life , span;blowup , of , cusp type;the envelope of characteristics

Abstract: In this paper we investigate the formation of singularities of hyperbolic systems. Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.

Key words: quasi-linear , systems;strictly , hyperbolic , systems;life , span;blowup , of , cusp type;the envelope of characteristics

中图分类号:

O175.27

王利珍. 拟线性可化约的双曲型方程组的奇性分析[J]. 数学季刊, 2005, 20(1): 10-20.

WANG Li-zhen. Analysis of Singularity for Reducible Quasi-linear Hyperbolic Systems[J]. Chinese Quarterly Journal of Mathematics, 2005, 20(1): 10-20.

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