[1]郑永树.对角型拟线性双曲组的整体经典解[J].华侨大学学报(自然科学版),2001,22(4):331-336.[doi:10.3969/j.issn.1000-5013.2001.04.001]
　Zheng Yongshu.Global Classical Solution to Quasi-Linear Hyperbolic System of Diagonal Form[J].Journal of Huaqiao University(Natural Science),2001,22(4):331-336.[doi:10.3969/j.issn.1000-5013.2001.04.001]
点击复制

对角型拟线性双曲组的整体经典解()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第22卷
期数:
2001年第4期
页码:
331-336
栏目:
出版日期:
2001-10-20

文章信息/Info

Title:
Global Classical Solution to Quasi-Linear Hyperbolic System of Diagonal Form
文章编号:
1000-5013(2001)04-0331-06
作者:
郑永树
华侨大学经济管理学院 泉州362011
Author(s):
Zheng Yongshu
College of Econ. Manag., Huaqiao Univ., 362011, Quanzhou
关键词:
拟线性双曲组;  柯西问题;  整体经典解
Keywords:
quasi-linear hyperbolic system;  Cauchy problem;  global classical solution
分类号:
O241.82
DOI:
10.3969/j.issn.1000-5013.2001.04.001
摘要:
研究对角型拟线性严格双曲组的柯西问题,其初值为 C1-模、L1-模和全变差均有界的函数 .证明如果方程组是弱线性退化时,对于小的初值在 t≥ 0存在唯一的整体经典解 .如果方程组不是弱线性退化的,给出其经典解的生命区间估计 .
Abstract:
A study is made on Cauchy problem of strictly quasi-linear hyperbolic system of diagonal form,of which the initial values are C 1-mode,L 1-mode and function with bounded total variation. As proved by the author,if the equation set are in weak linear degeneration,there exists unique global classical solution to small initial value at t≥0; if the equation set are not in weak linear degeneration,the life interval estimation of their classical solutions are given.

参考文献/References:

[1] John F. Formation of singularities in one-dimensional nonlinear wave propagation [J]. Communications on Pure and Applied Mathematics, 1974.377-405.doi:10.1002/cpa.3160270307.
[2] Hrmander L. The life span of classical solutions of nonlinear hyperbolic equations [J]. Institute Mittag-Leffer, 1985(5):87-96.
[3] Liu Taiping. Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differe-ntial equations [J]. Journal of Differential Equations, 1979.92-111.
[4] Li Tatsien, Zhou Yi, Kong Dexing. Weak linear degene racy and global classical solutions for general quasilinear hyperbolic systems [J]. Communications in Partial Differential Equations, 1994.1263-1317.doi:10.1080/03605309408821055.
[5] Li Tatsien, zhou Yi, Kong Dexing. Global classical solutions for general quasilinear hyperbolic systems with decay initial data [J]. Nonlinear Analysis-Theory Methods and Applications, 1997(8):1299-1332.
[6] 孔德兴. 对角型拟线性双曲组经典解的奇性形成及其生命区间 [J]. 河南大学学报(自然科学版), 1993(2):7-11.
[7] 李大潜, 俞文. 一阶拟线性双曲型方程组的柯西问题 [J]. 数学进展, 1963(2):152-171.
[8] Zheng Yongshu, Liu Fagui. A necessary and sufficient condition for global existence of classical solutions to Cauchy porblem of quasilinear hyperbolic systems in diagonal form [J]. ACTA MATHEMATICA SCIENTIA, 2000(4):571-576.

相似文献/References:

[1]伍锦棠,郑永树.带非线性松弛项的半线性双曲组的整体光滑解[J].华侨大学学报(自然科学版),2003,24(2):131.[doi:10.3969/j.issn.1000-5013.2003.02.004]
　Wu Jintang,Zheng Yongshu.Globally Smooth Solution to a Semi-Linear Hyperbolic System with a Nonlinear Relaxation Term[J].Journal of Huaqiao University(Natural Science),2003,24(4):131.[doi:10.3969/j.issn.1000-5013.2003.02.004]

备注/Memo

备注/Memo:
福建省自然科学基金资助项目
更新日期/Last Update: 2014-03-23