GLOBAL AND BLOW-UP SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH A GRADIENT TERM

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	GLOBAL AND BLOW-UP SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH A GRADIENT TERM
	Ding, Juntang 1,2; Guo, Bao-Zhu2,3
	2011
发表期刊	HOUSTON JOURNAL OF MATHEMATICS
ISSN	0362-1588
卷号	37 期号:4 页码:1265-1277
摘要	In this paper, we are concerned with the following nonlinear parabolic equation with a gradient term and Neumann boundary condition: {(b(u))(t) = del . (a(u)del u) + f(x, u,vertical bar del u vertical bar(2), t) in D x (0, T), partial derivative u/partial derivative n = 0 on partial derivative D x (0,T), u(x,0) = u(0)(x)>0 in (D) over bar, where D subset of R-N (N >= 2) is a bounded domain of R-N with smooth boundary partial derivative D. The upper and lower solution technique is adopted in investigations. The sufficient conditions for the existence of global positive solution and an upper estimate of global solution are given. Moreover, under some appropriate assumptions on the functions a, b, and f, we prove the existence of blow-up positive solution. An upper bound of "blow-up time" is also presented.
关键词	Parabolic equation gradient term global solution blow-up solution
语种	英语
资助项目	National Natural Science Foundation of China[61074048] ; National Natural Science Foundation of China[60974032] ; National Natural Science Foundation of China[61174082] ; National Natural Science Foundation of China[60874019] ; National Basic Research Program of China[2011CB808002] ; Shanxi Scholarship Council of China[2011-011] ; National Research Foundation of South Africa
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000300563600015
出版者	UNIV HOUSTON
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11826
专题	系统科学研究所
通讯作者	Ding, Juntang
作者单位	1.Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China 2.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa 3.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Ding, Juntang,Guo, Bao-Zhu. GLOBAL AND BLOW-UP SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH A GRADIENT TERM[J]. HOUSTON JOURNAL OF MATHEMATICS,2011,37(4):1265-1277.
APA	Ding, Juntang,&Guo, Bao-Zhu.(2011).GLOBAL AND BLOW-UP SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH A GRADIENT TERM.HOUSTON JOURNAL OF MATHEMATICS,37(4),1265-1277.
MLA	Ding, Juntang,et al."GLOBAL AND BLOW-UP SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH A GRADIENT TERM".HOUSTON JOURNAL OF MATHEMATICS 37.4(2011):1265-1277.