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带竞争势的非线性Klein—Gordon方程的稳定集和不稳定集
  • ISSN号：0254-3079
  • 期刊名称：《应用数学学报》
  • 时间：0
  • 分类：O175.27[理学—数学;理学—基础数学]
  • 作者机构：[1]四川师范大学数学与软件科学学院,成都610068
  • 相关基金：国家自然科学基金（10771151,10726034,10801102）和四川省青年科技基金（07ZQ026-009）.
作者： 蒋毅[1], 甘在会[1]
关键词： 非线性KLEIN-GORDON方程, 竞争势, 稳定集, 不稳定集, 整体解, 爆破, nonlinear Klein-Gordon equation, competing potential, stable set, unstable set, global existence, blowup
中文摘要：

本文研究带竞争势的非线性Klein—Gordon方程的柯西问题．首先定义了新的稳定集和不稳定集．其次证明了如果初值进入不稳定集，该柯西问题的解在有限时间内爆破；如果初值进入稳定集，该柯西问题的整体解存在．最后运用势井讨论，我们回答了当初值在什么范围时，该柯西问题的整体解存在这个问题．

英文摘要：

This paper deals with the Cauchy problem for the nonlinear Klein-Gordon equation with competing potentials. Firstly, we define new stable and unstable sets. Then we prove that if the initial data enter into the unstable set, then the solution of the aforementioned Cauchy problem blows up in finite time, and if the initial data enter into the stable set, then the solution of the aforementioned Cauchy problem globally exists. Finally, by using scaling argument, we answer the question： which domain are the initial data in, the global solution to the Cauchy problem exists.

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期刊信息
  • 《应用数学学报》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国数学会 中国科学院数学与系统科学研究院
  • 主编：丁夏畦
  • 地址：北京市海淀区中关村东路55号
  • 邮编：100190
  • 邮箱：
  • 电话：
  • 国际标准刊号：ISSN：0254-3079
  • 国内统一刊号：ISSN：11-2040/O1
  • 邮发代号:2-822
  • 获奖情况:
  • 1996、2000年获“中科院优秀科技期刊”三等奖,1997年获“第二届全国优秀科技期刊”三等奖,2001年入选“双效期刊”（中国期刊方阵）
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:6864