华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (2): 131-134.

• 数学 • 上一篇    下一篇

条件非线性最优扰动的最大值原理

刘永明1,2,3   

  1. 1. 华东师范大学 地理信息科学教育部重点实验室,上海 200062; 2. 华东师范大学 数学系, 上海 200241; 3. 中国科学院 大气物理研究所, 北京 100029
  • 收稿日期:2007-11-27 修回日期:2008-01-25 出版日期:2008-03-25 发布日期:2008-03-25
  • 通讯作者: 刘永明

Maximum principle of conditional optimal nonlinear perturbation(Chinese)

LIU Yong-ming   

  1. 1. Key Laboratory of Geographic Information Sciences,Ministry of Education, East China Normal University, Shanghai 200062, China; 2. Department of Mathematics, East China Normal University, Shanghai 200241, China; 3. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
  • Received:2007-11-27 Revised:2008-01-25 Online:2008-03-25 Published:2008-03-25
  • Contact: LIU Yong-ming

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摘要： 在非线性系统(发展方程及常微分方程)中初始数据的扰动对系统以后某固定时刻,T的状态的影响是一个重要的研究课题.本文研究非线性系统在初始数据在一定的范围(称为初始扰动域)内作有限幅度的扰动时,在时刻,T对状态扰动的幅度达到最大的问题.通过考虑反向时间的问题及假设解对初始数据的连续依赖性,证明了若在时刻,T状态扰动的幅度达到最大, 则初始数据位于初始扰动域的边界上, 这个结果的重要意义在于可以减少数值求解扰动幅度最大问题的计算量.

关键词: 变分法, 条件非线性最优扰动, 最大值原理, 变分法, 条件非线性最优扰动, 最大值原理

Abstract: The effect of initial data on the state of nonlinear systems (evolution equation and ordinary differential equations) at a fixed later time T is an important subject to study. The maximum norm of disturbances at time T when the finite amplitude of initial data disturbances restricted in a region (called the initial disturbance region) is studied. By considering the solutions to the problems of backwards in time and the hypothesizing the continuously dependence of solutions to the initial dada, it is proved that if the maximum norm of disturbances at time T is attained, then the initial data are at the boundary of the initial disturbance region. The importance of the results is on reducing the computation labor of the maximum norm of the disturbances.

Key words: conditional optimal nonlinear perturbation, maximum principle, calculus of variation, conditional optimal nonlinear perturbation, maximum principle

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