期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

Lipschitz Continuous Solutions to the Cauchy Problem for Quasi-linear Hyperbolic Systems

Lipschitz Continuous Solutions to the Cauchy Problem for Quasi-linear Hyperbolic Systems
原文传递
导出
摘要 Lipschitz continuous solutions to the Cauchy problem for 1-D first order quasi-linear hyperbolic systems are considered. Based on the methods of approximation and integral equations, the author gives two definitions of Lipschitz solutions to the Cauchy problem and proves the existence and uniqueness of solutions. Lipschitz continuous solutions to the Cauchy problem for 1-D first order quasi- linear hyperbolic systems are considered. Based on the methods of approximation and integral equations, the author gives two definitions of Lipschitz solutions to the Cauchy problem and proves the existence and uniqueness of solutions.
作者 Xiang CHEN
机构地区 School of Mathematical Sciences
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2012年第4期521-536,共16页 数学年刊（B辑英文版）
关键词 CAUCHY问题 拟线性双曲系统 LIPSCHITZ连续 连续解 解的存在性 积分方程 一阶 First order quasi-linear hyperbolic systems, Lipschitz continuous solution,Cauchy problem, Existence and uniqueness
分类号 O175.27 [理学—基础数学] O177.91 [理学—基础数学]
  • 相关文献

参考文献20

  • 1Cesari, L., A boundary-value problem for quasilinear hyperbolic systems in the Schauder canonic form, Ann. Squola Norm. Sup. Pisa, 4(1), 1974, 311-358.
  • 2Cirin, M., Nonlinear hyperbolic problems with solutions on preassigned sets, Michigan Math. J., 17, 1970, 193 209.
  • 3Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations, McGraw-Hill Book Com- pany, Inc., New York, Toronto, London, 1955.
  • 4Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. II, Wiley, New York, 1962.
  • 5Courant, R, and Lax, P., Cauchy's problem for nonlinear hyperbolic differential equations in two indepen- dent variables, Annali di matmatica, 40, 1955, 161-166.
  • 6Douglis, A., Some existence theorems for hyperbolic systems of partial differential equations in two inde- pendent variables, Comm. Pure Appl. Math., 5, 1952, 119-154.
  • 7Donglis, A., The continuous dependence of generalized solutions of non-linear partial differential equations upon initial data, Comm. Pure Appl. Math., 14, 1961, 267-284.
  • 8Evans L. C. and Cariepy, R. F., Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, FL, 1992.
  • 9Hartman, P. and Wintner, A., On hyperbolic partial differential equations, Amer. J. Math., 74, 1952, 834-864.
  • 10Hoff, D., Locally Lipschitz solutions of a single conservation law in several space variables, J. Diff. Eq., 42(2), 1981, 215 -233.
Chinese Annals of Mathematics,Series B
2012年 第4期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部