Global existence and blow-up solutions for quasilinear reaction-diffusion equations with a gradient term

doi:10.1016/j.aml.2010.12.052

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	Global existence and blow-up solutions for quasilinear reaction-diffusion equations with a gradient term
	Ding, Juntang 1; Guo, Bao-Zhu1,2,3
	2011-06-01
发表期刊	APPLIED MATHEMATICS LETTERS
ISSN	0893-9659
卷号	24 期号:6 页码:936-942
摘要	In this work, we study the blow-up and global solutions for a quasilinear reaction-diffusion equation with a gradient term and nonlinear boundary condition: {(g(u))(t) = Delta u + f (x, u, vertical bar del u vertical bar(2) t) in D x (0, T). partial derivative u/partial derivative n = r(u) 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. Through constructing suitable auxiliary functions and using maximum principles, the sufficient conditions for the existence of a blow-up solution, an upper bound for the "blow-up time", an upper estimate of the "blow-up rate", the sufficient conditions for the existence of the global solution, and an upper estimate of the global solution are specified tinder some appropriate assumptions on the nonlinear system functions f, g, r, and initial value u(0). (C) 2011 Elsevier Ltd. All rights reserved.
关键词	Reaction-diffusion equation Blow-up solution Global solution Gradient term
DOI	10.1016/j.aml.2010.12.052
语种	英语
资助项目	National Natural Science Foundation of China[61074048] ; National Natural Science Foundation of China[60974032] ; National Basic Research Program of China[2011CB808002] ; Natural Science Foundation of Shanxi Province ; Shanxi Scholarship Council of China
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000288883800026
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/12378
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 Johannesburg, South Africa
推荐引用方式 GB/T 7714	Ding, Juntang,Guo, Bao-Zhu. Global existence and blow-up solutions for quasilinear reaction-diffusion equations with a gradient term[J]. APPLIED MATHEMATICS LETTERS,2011,24(6):936-942.
APA	Ding, Juntang,&Guo, Bao-Zhu.(2011).Global existence and blow-up solutions for quasilinear reaction-diffusion equations with a gradient term.APPLIED MATHEMATICS LETTERS,24(6),936-942.
MLA	Ding, Juntang,et al."Global existence and blow-up solutions for quasilinear reaction-diffusion equations with a gradient term".APPLIED MATHEMATICS LETTERS 24.6(2011):936-942.