具有非局部源的快扩散方程组解的熄灭

王娟; 陈玉娟; 张海星; 陆晨

doi:10.3879/j.issn.1000-0887.2013.04.011

具有非局部源的快扩散方程组解的熄灭

doi: 10.3879/j.issn.1000-0887.2013.04.011

南通大学理学院, 江苏南通 226007

基金项目: 国家自然科学基金资助项目(11271209); 江苏省教育厅自然科学(面上)基金资助项目(12KJB110018);2013年江苏省政府留学奖学金项目;全国大学生实践创新计划基金资助项目(201210304005)

详细信息

作者简介:
王娟(1979—), 女, 江苏南通人, 硕士生(E-mail:tzsgwjg@126.com);陈玉娟(1969—), 女, 江苏南通人, 教授(通讯作者. E-mail:nttccyj@ntu.edu.cn).

中图分类号: O175.29
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出版历程
- 收稿日期: 2013-02-02
- 修回日期: 2013-03-19
- 刊出日期: 2013-04-15

Extinction for a Class of Fast Diffusion System With Nonlocal Sources

School of Sciences, Nantong University, Nantong, Jiangsu 226007, P.R.China

摘要

摘要: 利用上下解的方法和积分估计, 研究了一类具有非局部源的快扩散方程组解熄灭的充分条件,证明当参数和初值满足一定条件时，解在有限时刻发生熄灭．
- 快扩散方程组 /
- 熄灭 /
- 非局部源
Abstract: The sufficient conditions for the extinction of solutions of a class of fast diffusion system with nonlocal sources were investigated, where the upper and lower solution method and integral estimates were used. It is shown that when the initial values and the parameters satisfy some conditions, the solution of the system extincts in finite time.
- fast diffusion system /
- extinction /
- nonlocal sources

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参考文献(19)

[1]	Kalashnikov A S.Some problems of the qualitative theory of second order nonlinear degenerate parabolic equations[J].Uspekhi Mat Nauk,1987, 42(2): 135-176.
[2]	顾永耕. 抛物方程的解的熄灭的充要条件[J]. 数学学报, 1994, 37(1): 73-79.（GU Yong-geng. Necessary and sufficient conditions of extinction of solution on parabolic equations[J].Acta Math Sinica,1994, 37(1): 73-79.(in Chinese)）
[3]	Peletier L A, Zhao J N. Large time behavior of solution of the porous media equation with absorption: the fast diffusion case[J].Nonlinear Anal,1991, 17(10): 991-1009.
[4]	Galaktionov V A, Vazquez J L. Asymptotic behaviour of nonlinear parabolic equations with critical exponents[J].A Dynamical System Approach, J Funct Anal,1991, 100(2): 435-462.
[5]	Galaktionov V A, Vazquez J L.Extinction for a quasilinear heat equation with absorption I[J]. Technique of Intersection Comparison Comm Partial Differential Equations,1994, 19(7/8): 1075-1106.
[6]	Galaktionov V A, Vazquez J L.Extinction for a quasilinear heat equation with absorption II[J]. A Dynamical System Approach Comm Partial Differential Equations,1994, 19(7/8): 1107-1137.
[7]	Tian Y, Mu C L.Extinction and nonextinction for ap-Laplacian equation with nonlinear source[J].Nonlinear Anal,2008, 69(8): 2422-2431.
[8]	Ferreira R, Vazquez J L.Extinction behavior for fast diffusion equations with absorption[J].Nonlinear Anal,2001, 43(8): 943-985.
[9]	Yin J X, Li J, Jin C H.Non-extinction and critical exponent for a polytropic filtration equation[J].Nonl Anal,2009, 71(1/2): 347-357.
[10]	Yin J X, Jin C H.Critical extinction and blowup exponents for fast diffusive polytropic filtration equation with sources[J]. Proc Edinburgh Math Soc,2009, 52(2): 419-444.
[11]	Yin J X, Jin C H.Critical extinction and blow-up exponents for fast diffusivep-Laplacian with sources[J].Math Method Appl Sci,2007, 30(10): 1147-1167.
[12]	Yuan H J, Lian S Z, Gao W J, Xu X J, Cao C L. Extinction and positive for the evolutionp-Laplacian equation in R-N [J]. Nonl Anal TMA,2005, 60(6): 1085-1091.
[13]	Han Y Z, Gao W J.Extinction for a fast diffusion equation with a nonlinear nonlocal source[J].Arch Math,2011, 97(4): 353-363.
[14]	Friedman A, Mcleod B.Blow-up of positive solutions of semilinear heat equations[J].Indiana Univ Math J,1985, 34(2): 425-447.
[15]	Furter J, Grinfeld M.Local vs nonlocal interactions in population dynamics[J].J Math Biology,1989, 27(1): 65-80.
[16]	Lu H L, Wang M X. Global solutions and blowup problems for a nonlinear degenerate parabolic system coupled via nonlocal sources[J].J Math Anal Appl,2007, 333(2): 984-1007.
[17]	Zheng S N, Wang L D. Blowup rate and profile for a degenerate parabolic system coupled via nonlocal sources[J]. Comput Math Appl,2006, 52(10/11): 1387-1402.
[18]	Deng W B, Li Y X, Xie C H.Blow-up and global existence for a nonlocal degenerate parabolic system[J].J Math Anal Appl,2003, 277(1): 199-217.
[19]	Du L L.Blow-up for a degenerate reactiondiffusion system with nonlinear nonlocal sources[J].J Comput Appl Math,2007, 202(2): 237-247.