浅水波方程强解的唯一延拓性质

journal6 ›› 2011, Vol. 32 ›› Issue (2): 13-18.

浅水波方程强解的唯一延拓性质

（湘潭大学数学系，湖南湘潭 411105）

出版日期:2011-03-25 发布日期:2012-04-09
作者简介:朱年花(1984-),女,山东人,湘潭大学数学系硕士研究生,主要从事偏微分方程研究.
基金资助:
国家自然科学基金资助项目（1077108）

Unique Continuation of Strong Solutions of Shallow Water Equations

(School of Mathematics and Computational Sciences,Xiangtan University,Xiangtan 411105,Hunan China)

Online:2011-03-25 Published:2012-04-09

摘要/Abstract

摘要：考虑某些浅水波方程初值问题强解的唯一延拓性质,即证明了若在初始及以后某一时刻,强解的空间导数呈指数衰退,则它是零解.特别地,初值有紧支集的柯西问题的强解在以后的时间没有紧支集除非它是零解.

关键词： 浅水波方程, 强解, 唯一延拓性

Abstract: It is shown that strong solutions of shallow water equations,initially decaying exponentially together with its spacial derivative,must be identically equal to zero if it also decays exponentially at a later time.In particular,a strong solution of the Cauchy problem with compact initial profile can not be compactly supported at any later time unless it is the zero solution.

Key words: shallow water equation, strong solution, unique continuation

朱年花. 浅水波方程强解的唯一延拓性质[J]. journal6, 2011, 32(2): 13-18.

ZHU Nian-Hua. Unique Continuation of Strong Solutions of Shallow Water Equations[J]. journal6, 2011, 32(2): 13-18.