Blow-up and global existence for nonlinear parabolic equations with Neumann boundary conditions

doi:10.1016/j.camwa.2010.05.015

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	Blow-up and global existence for nonlinear parabolic equations with Neumann boundary conditions
	Ding, Juntang 1; Guo, Bao-Zhu1,2,3
	2010-08-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	60 期号:3 页码:670-679
摘要	In this paper, we study the global and blow-up solutions of the following problem: {(h(u))(t) = del center dot (a(u, t)b(x)del u) + g(t)f(u) 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) is a bounded domain with smooth boundary partial derivative D. By constructing auxiliary functions and using maximum principles and comparison principles, the sufficient conditions for the existence of global solution, an upper estimate of the global solution, the sufficient conditions for the existence of the blow-up solution, an upper bound for the "blow-up time", and an upper estimate of the "blow-up rate" are specified under some appropriate assumptions on the functions a. b, f. g. and h. (C) 2010 Elsevier Ltd. All rights reserved.
关键词	Parabolic equation Global solution Blow-up solution Neumann boundary condition
DOI	10.1016/j.camwa.2010.05.015
语种	英语
资助项目	National Natural Science Foundation of China ; Natural Science Foundation of Shanxi Province ; Foundation of Shanxi Province for Overseas Returned Scholars
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000280935400026
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10195
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.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Wits, Johannesburg, South Africa
推荐引用方式 GB/T 7714	Ding, Juntang,Guo, Bao-Zhu. Blow-up and global existence for nonlinear parabolic equations with Neumann boundary conditions[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2010,60(3):670-679.
APA	Ding, Juntang,&Guo, Bao-Zhu.(2010).Blow-up and global existence for nonlinear parabolic equations with Neumann boundary conditions.COMPUTERS & MATHEMATICS WITH APPLICATIONS,60(3),670-679.
MLA	Ding, Juntang,et al."Blow-up and global existence for nonlinear parabolic equations with Neumann boundary conditions".COMPUTERS & MATHEMATICS WITH APPLICATIONS 60.3(2010):670-679.