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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (1): 123-127.doi: 10.6040/j.issn.1671-9352.0.2015.003

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Nehari流形在一类半线性抛物方程爆破中的应用

刘洋,达朝究,李富明   

  1. 西北民族大学数学与计算机科学学院, 甘肃 兰州 730124
  • 收稿日期:2015-01-12 出版日期:2016-01-16 发布日期:2016-11-29
  • 作者简介:刘洋(1983— ),男,硕士,讲师,研究方向为非线性发展方程. E-mail:xuezhongjing7890@aliyun.com
  • 基金资助:
    国家自然科学基金资助项目(41465002);中央高校基本科研业务费专项资金资助项目(31920150036,31920150083)

Nehari manifold and application to blow-up for a class of semilinear parabolic equations

LIU Yang, DA Chao-jiu, LI Fu-ming   

  1. College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, Gansu, China
  • Received:2015-01-12 Online:2016-01-16 Published:2016-11-29

摘要: 研究了一类半线性抛物方程的初边值问题,在具有正初始能量的情况下,通过Nehari流形与凸性方法得到了解的有限时间爆破,进而刻画了初始能量与有限时间爆破的关系。

关键词: Nehari流形, 有限时间爆破, 半线性抛物方程

Abstract: The initial boundary value problem for a class of semilinear parabolic equations with positive initial energy is studied. The finite time blow-up of solutions is obtained by the Nehari manifold and the convexity method. Moreover, the relationship between initial energy and finite time blow-up of solutions is described.

Key words: semilinear parabolic equations, finite time blow-up, Nehari manifold

中图分类号: 

  • O175.24
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