数学物理学报 ›› 2016, Vol. 36 ›› Issue (6): 1145-1156.

• 论文 • 上一篇    下一篇

与Fisher-Kolmogorov's方程相关的一个差分方程的最快异宿解

徐嘉1, 王燕霞2, 代国伟3   

  1. 1. 西北师范大学体育学院 兰州 730070;
    2. 西北师范大学数学与统计学院 兰州 730070;
    3. 大连理工大学数学科学学院 辽宁大连 116024
  • 收稿日期:2016-03-12 修回日期:2016-07-15 出版日期:2016-12-26 发布日期:2016-12-26
  • 通讯作者: 代国伟 E-mail:daiguowei@dlut.edu.cn
  • 基金资助:

    国家自然科学基金(11261052,11401477,11201378)资助

Fast Heteroclinic Solutions for a Difference Equation Related to Fisher-Kolmogorov's Equation

Xu Jia1, Wang Yanxia2, Dai Guowei3   

  1. 1. College of Physical Education, Northwest Normal University, Lanzhou 730070;
    2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070;
    3. School of Mathematical Sciences, Dalian University of Technology, Liaoning Dalian 116024
  • Received:2016-03-12 Revised:2016-07-15 Online:2016-12-26 Published:2016-12-26
  • Supported by:

    Supported by the NSFC (11261052,11401477,11201378)

摘要:

该文运用变分法证明了与Fisher-Kolmogorov's方程行波解相关的一个二阶差分方程最快异宿解的存在性.获得了能量泛函在加权Hilbert空间上的最小值点,即最快异宿解.

关键词: 最快异宿解, 变分法, 差分方程

Abstract:

In this paper, we prove the existence of fast heteroclinic solutions for a second-order difference equation related to traveling wave solutions of Fisher-Kolmogorov's equation. By means of variational approach, the fast heteroclinic solutions are obtained as minimizers of an energy functional on a weighted Hilbert space.

Key words: Fast heteroclinic solutions, Variational method, Difference equation

中图分类号: 

  • O175.7