数学物理学报 ›› 2004, Vol. 24 ›› Issue (3): 265-274.

• 论文 • 上一篇    下一篇

带时滞的退化非线性抛物方程的熄灭

 陈友朋, 谢春红   

  1. 南京师范大学数学系 江苏南京 210097 盐城师范学院数学系 江苏盐城 224002 南京大学数学系 江苏南京 210093
  • 出版日期:2004-06-22 发布日期:2004-06-22

Quenching for a Nonlinear Degenerate Parabolic Equation with Time Delay

 CHEN You-Peng, XIE Chun-Hong   

  • Online:2004-06-22 Published:2004-06-22

摘要:

该文研究一带时滞的退化非线性抛物方程的初边值问题。运用正则化方法和上下解技巧证明了上述问题的古典正解的局部存在性及其可延拓性。讨论了整体存在性和 有限时刻熄灭,建立了临界长度,得到了熄灭点的位置以及特殊f(u)情形下的熄灭速率估计。

关键词: 退化抛物方程;时滞;上下解;临界长度;熄灭速率

Abstract:

This paper deals with the initial boundary valu e problem of a nonlinear degenerate parabolic equation with time delay.The method of regularization and the technique of upper and lower solutions are employed to show the local existence and the continuation of the positive classical solution of the above problem.The global existence and finite time quenching are discussed, and the critical length is established.The location of the uenching points and the estimates of the quenching rate for the special case of f(u) are obtained.

Key words: Degenerate parabolic equation, Time delay, Upper and lower solutions, Critical l ength, Quenching rate

中图分类号: 

  • 35K55