The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics

被引：29

作者：

Li, TT ^{[1
]}

Peng, YJ

机构：

[1] Fudan Univ, Dept Math, Shanghai 200433, Peoples R China

[2] Univ Clermont Ferrand, CNRS, Lab Math Appl, UMR 6620, F-63177 Clermont Ferrand, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2003年 / 52卷 / 02期

关键词：

mixed initial-boundary value problem; reducible quasilinear hyperbolic system; linearly degenerate system; formation of singularity;

D O I：

10.1016/S0362-546X(02)00123-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove that the C-0 boundedness of solution implies the global existence and uniqueness of C-1 solution to the mixed initial-boundary value problem for linearly degenerate, reducible quasilinear hyperbolic systems with nonlinear boundary conditions and we show by an example that the C-0 norm of solution may blow up in a finite time. This gives the mechanism of the formation of singularities caused by the interaction of boundary conditions with nonlinear hyperbolic waves. The same result is still valid for the quasilinear hyperbolic system of rich type. (C) 2002 Elsevier Science Ltd. All rights reserved.

引用

页码：573 / 583

页数：11