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.
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.
基金
Supported by the NSFC(1001024)
关键词
准线性系统
严格双曲线系统
偏微分方程
奇异性
存在性
尖点类型
quasi-linear systems
strictly hyperbolic systems
life span
blowup of cusp type
the envelope of characteristics
