一个退化抛物双曲方程柯西问题熵解的唯一性

上海交通大学学报（自然版） ›› 2011, Vol. 45 ›› Issue (07): 1085-1090.

一个退化抛物双曲方程柯西问题熵解的唯一性

郝兴文1,2，王钦1

(1. 上海交通大学数学系，上海 200240；2. 潍坊学院数学与信息科学学院，山东潍坊 261061)

收稿日期:2010-06-10 出版日期:2011-07-29 发布日期:2011-07-29
基金资助:
国家自然科学基金资助项目(10571120,10971135),上海市曙光项目(06SG11)、潍坊学院博士基金项目（2011BS11）

Uniqueness of the Entropy Solutions to Cauchy Problem for a Degenerate Parabolic-Hyperbolic Equation

HAO Xing-Wen-1, 2 , WANG Qin-1

(1. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China; 2. School of Mathematics and Information Sciences, Weifang University, Weifang 261061, Shandong, China)

Received:2010-06-10 Online:2011-07-29 Published:2011-07-29

摘要/Abstract

摘要： Kuznetsov方法是估计双曲型方程熵解与它的数值解之间误差的有效方法，文中应用该方法证明一个二阶退化抛物双曲方程熵解的唯一性，并用双变量方法得到了熵解在初值的L1连续性.

关键词: Kuznetsov方法, 退化抛物双曲方程, 熵解, 误差估计

Abstract: Kuznetsov’s method is a useful tool to establish the error estimate between numerical solutions and entropy weak solution for hyperbolic equation. This paper uses this method to prove the uniqueness to the Cauchy problem of a special example of second order degenerate parabolic-hyperbolic equation, Meanwhile, the paper obtained that entropy solutions are continuous at t=0 in the sense of L1 norm by the double variable device.

Key words: Kuznetsov method, degenerate parabolichyperbolic equation, entropy solutions,, error estimate

中图分类号:

O175.27

郝兴文1, 2, 王钦1. 一个退化抛物双曲方程柯西问题熵解的唯一性[J]. 上海交通大学学报（自然版）, 2011, 45(07): 1085-1090.

HAO Xing-Wen-1, 2 , WANG Qin-1. Uniqueness of the Entropy Solutions to Cauchy Problem for a Degenerate Parabolic-Hyperbolic Equation[J]. Journal of Shanghai Jiaotong University, 2011, 45(07): 1085-1090.

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