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一类具有Dirichlet边界条件的振幅方程的稳定性与分岔研究
  • ISSN号：1001-9847
  • 期刊名称：《应用数学》
  • 时间：0
  • 分类：O193[理学—数学;理学—基础数学]
  • 作者机构：[1]南京农业大学理学院,江苏南京210095, [2]洛阳师范学院数学科学学院,河南洛阳471022
  • 相关基金：Supported by the National Natural Science Foundation of China（11171158）, the Fundamental Research Funds for the Central Universities（KYZ201538） and the Natural Science Foundation of Jiangsu Province（BK201506051）
作者： 石磊[1], 刘乐[2]
关键词： 分岔, 稳定性, 振幅方程, 特征值问题, Bifurcation, Stability, Amplitude equation, Eigenvalue problem
中文摘要：

本文研究一个偏微分方程组的平凡稳态解（0,0）的稳定性和分岔的问题,所研究的方程组是一个定义在有界区域（0,L）上有着Dirichlet边界条件的振幅方程.文中区间长度L被看成是一个分岔参数.文章考虑平凡稳态解（0,0）处的渐近行为,利用扰动理论的方法,获得非平凡解分岔结果,进一步地分析了非平凡分岔解的稳定性及其渐近行为.

英文摘要：

This paper focuses on the bifurcation and stability of the trivial solution （0,0） of a particular system of parabolic partial differential equations. The equation is as an amplitude equation on a bounded domain （0, L） with Dirichlet boundary conditions. In this paper, the asymptotic behavior of the stationary solution （0,0） of the amplitude equation is considered. With the length L of the domain considered as bifurcation parameter, branches of nontrivial solutions are shown by the perturbation method. Besides, in this paper, a study is made on local behavior of these branches. Moreover, the stability of the bifurcated solutions are analyzed as well.

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地球流体力学和物理学中一些非线性偏微分方程研究
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期刊信息
  • 《应用数学》
  • 北大核心期刊（2011版）
  • 主管单位:国家教育部
  • 主办单位:华中科技大学
  • 主编：李大潜
  • 地址：武汉珞喻路1037号华中科技大学逸夫科技大楼南楼902室
  • 邮编：430074
  • 邮箱：yysx_hust@163.com
  • 电话：027-87543831
  • 国际标准刊号：ISSN：1001-9847
  • 国内统一刊号：ISSN：42-1184/O1
  • 邮发代号:38-61
  • 获奖情况:
  • 中国科学引文数据库来源期刊,中国学术期刊综合评价数据库来源期刊
  • 国内外数据库收录:
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  • 被引量:4139