数学物理学报 ›› 2014, Vol. 34 ›› Issue (5): 1061-1070.

• 论文 • 上一篇    下一篇

具有正边界值的一类退化抛物方程组解的爆破与全局有界

凌征球|覃思乾   

  1. 玉林师范学院 数学与信息科学学院 广西玉林 537000
  • 收稿日期:2012-08-31 修回日期:2014-07-25 出版日期:2014-10-25 发布日期:2014-10-25
  • 基金资助:

    广西高校科学技术研究重点项目(ZD2014106)资助.

Blow-up and Global Boundedness for a Degenerate Parabolic System with Positive Boundary Value Condition

 LING Zheng-Qiu, QIN Sai-Qan   

  1. Institute of Mathematics and Information Science, Yulin Normal University, Guangxi Yulin 537000
  • Received:2012-08-31 Revised:2014-07-25 Online:2014-10-25 Published:2014-10-25
  • Supported by:

    广西高校科学技术研究重点项目(ZD2014106)资助.

摘要:

该文研究具有正边界值条件的一类非局部退化抛物型方程组. 借助于上下解方法和分段函数, 获得了方程组解的全局有界与
爆破准则. 结果表明, 正的边界值ε0在确定方程组解的爆破中起着关键的作用.

关键词: 退化抛物型方程组, 爆破, 全局有界

Abstract:

This paper deals with a degenerate parabolic system coupled via nonlocal sources, subjecting to positive Dirichlet boundary value conditions. With the help of the super and sub-solution methods and the piecewise function, the blow-up criteria and global boundedness of nonnegative solutions are determined. The results show that the positive boundary value εplays an important role in the case of blow-up.

Key words: Degenerate parabolic system, Blow-up, Global boundedness

中图分类号: 

  • 35K40