[1]陈友朋.带时滞的退化半线性抛物方程的熄灭(英文)[J].南京师大学报(自然科学版),2006,29(01):7-13.
　Chen Youpeng.Quenching for Degenerate Semilinear Parabolic Equations with Time Delay[J].Journal of Nanjing Normal University(Natural Science Edition),2006,29(01):7-13.
点击复制

带时滞的退化半线性抛物方程的熄灭(英文)()
分享到：

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第29卷
期数:
2006年01期
页码:
7-13
栏目:
数学
出版日期:
2006-03-30

文章信息/Info

Title:
Quenching for Degenerate Semilinear Parabolic Equations with Time Delay
作者:
陈友朋1; 2
(1. 盐城师范学院数学系,江苏盐城224002)
(2. 南京师范大学数学与计算机科学学院,江苏南京210097)
Author(s):
Chen Youpeng 1; 2
(1. Department ofMathematics, Yancheng Normal Institute, Yancheng 224002, China)
(2. School ofMathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China)
关键词:
熄灭问题;  退化半线性抛物方程;  时滞;  临界长度;  简单估计
Keywords:
quenching p roblem;  degenerate semilinear parabolic equation;  time delay;  critical length;  a simp le estimate
分类号:
O175.26
摘要:
考虑带时滞的退化半线性抛物方程的熄灭问题.利用正则化方法和上下解技巧,我们得到了上述问题经典解的存在惟一性,同时还证明了存在一个临界长度a*使得上述问题的解u当a<a*时整体存在,而当a>a*时在有限时间内熄灭.进而我们还得到关于临界长度a*的一个简单估计.
Abstract:
This paper dealswith the quenching p roblem for degenerate semilinear parabolic equationswith time delay. By using regularizationmethod and upper and lower solutions’ technique, we obtain the existence of a unique classical so2 lution to the above p roblem and p rove that there exists a critical length a *such that the solution u of the above p roblem exists globally for a < a *and quenches in finite time for a > a * . Furthermore, we also get a simp le estimate on the criti2 cal length a *.

参考文献/References:

[ 1 ] 　Pao C V. Nonlinear Parabolic and Ellip tic Equations[M ]. New York: Plenum Press, 1992.
[ 2 ] 　Sheng Q, Khaliq A Q. A compound adap tive app roach to degenerate nonlinear quenching p roblems[ J ]. NumerMethods for PartialDifferential Equations, 1999, 15 (1) : 29—47.
[ 3 ] 　Karawada H. On solutions of initial boundary p roblem for ut = uxx + 1/ 1 - u [ J ]. Publ R IMS Kyoto Univ, 1975, 15: 729— 736.
[ 4 ] 　AckerA, WalterW. The Quenching Problem forNonlinear PartialDifferential Equations[M ]. Lecture Notes inMath, Ber- lin: Sp ringer2Verlag , 1976.
[ 5 ] 　Chan C Y, Ke L, Vatsala A S. Impulsive quenching for reaction diffusion equations[ J ]. Nonlinear Anal, 1994, 22 (11) : 1323—1328.
[ 6 ] 　Chan C Y, Kong P C. Quenching for degenerate semilinear parabolic equations[ J ]. App licable Analysis, 1994, 52 ( 1) : 17—25.
[ 7 ] 　Deng K. Dynamical behaviour of solutions of a semilinear heat equation with nonlocal singularity[ J ]. SIAM J Math Anal, 1995, 26 (1) : 98—111.
[ 8 ] 　Ke L, Ning S. Quenching for degenerate parabolic equations[ J ]. NonlinearAnal, 1998, 34 (7) : 1123—1135.
[ 9 ] 　Pao C V. Quenching p roblem of a reaction-diffusion equation with time delay[ J ]. NonlinearAnal, 2000, 41 (1 /2) : 133— 142.
[10 ] 　Chan C Y, L iu H T. Global existence of solutions for degenerate semilinear parabolic p roblem[ J ]. NonlinearAnal, 1998, 34 (4) : 617—628.
[ 11 ] 　Chen Y P. Quenching for a degenerate and singular parabolic equation with time delay[ J ]. Journal of Nanjing University Mathematical Biquarterly, 2003, 20 (2) : 139—150.
[ 12 ] 　FloaterM S. Blow up at the boundary for degenerate semilinear parabolic equations [ J ]. Arch RatMech Anal, 1991, 114 (1) : 57—77.
[ 13 ] 　Friedman A. PartialDifferential Equations of Parabolic Type[M ]. Inc Englewood Cliffs: Prentice2Hall, 1964.
[ 14 ] 　Martel Y, Soup let P h. Small time boundary behavior of solutions of parabolic equations with noncompatible data [ J ]. J Math Pures App l, 2000, 79 (6) : 603—632.
[ 15 ] 　陈友朋. 一类退化的反应扩散方程的熄灭问题[ J ]. 南京大学学报数学半年刊, 1999, 16 (1) : 133—143.

备注/Memo

备注/Memo:
Foundation item: Supported Partially by the Research Program of the Natural Science of the Universitiesin Jiangsu Province (05KJB110144) .
Biography: Chen Youpeng, born in 1966, doctor, associate professor, majored in nonlinear partial differential equations.
E-mail: youpengc@yahoo. com. cn
更新日期/Last Update: 2013-05-05