Singular Solutions of the Cauchy Problem for SemilinearParabolic Equations with Singular Potentions

具奇异位势的半线性抛物方程Cauchy问题的奇异解(英文)

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摘要 In this paper we consider the Cauchy problem for the singular semilinear parabolic equation u t-Δu+V 1(x)u=V 2(x)u p,x∈R n\{0},t>0, where V 1(x),V 2(x) may have singularities at the origin. Using functions of the Kato class and the Green tight functions we got the existence of the positive solution being singular at the origin.

作者曾有栋陈祖墀

机构地区中国科学技术大学数学系

出处《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第1期1-8,共8页 数学季刊（英文版）

基金 SupportedbytheNationalNaturalScienceFoundationofChina(10 0 710 80 ) SupportedbytheFundofEducationMinistry

关键词 SINGULARITY Kato class Green tight function fixed point 异位势半线性势物方程 Cauchy问题奇异解 Kato类 GreenTight函数不动点

分类号 O175.26 [理学—基础数学]

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1FUJITA H. On the blowing up ofsolutions of the cauchy problem for ut=Δu+u1+α[J]. J Fac Sci Univ Tokyo section AMath,1996,13(1):109-124.
2FUITA H. On some nonexistence and nonuniqueness theorem for nonlinear parabolicequations[C]. Proc Symp Pure Math AMS,1969,18(1):105-113.
3KOBAYASHI K,SIRAO T,TANAKA H. On the growing up problem for semilinear heatequations[J]. J Math soc Japan,1977,29(3):407-424.
4WEISSLER F B. Local existence and nonexistence for semilinear parabolic equation isLp[J]. Indiana Univ Math J,1980,29(1):79-102.
5WEISSLER F B. Existence and nonexistence of global solutions for a semilinear heatequtions[J]. Isteal J of math,1981,28(1-2):29-40.
6LEVINE H A. Some nonexistence and instability theorems for solutions of formallyparabolic equations of the form Put=-Au+F(u)[J]. Arch Rat Mech Anal,1973,51(3):371-386.
7GIGA Y,KOHN R. Asymptoticall self-similar blow-up of semilinear heat equations[J].Comm Pure Appl Math,1985,38(3):297-319.
8LEVING H A. The role of critical exponets in blowup theorems[J]. SIAMReview,1990,32(2):262-288.
9LIU Y C. The existence and non-existence of global solutions to semilinear heatequations(in Chinese)[J]. China Math Ann,1997,18A(1):65-72.
10WANG M X, DING X X. The global solutions of semilinear heat equations,Aymptoticity and blow-up problem(in Chines)[J]. Science Sinica,1992,35A(10):1026-1034.

1李志阐,杨春鹏.薛定锷方程解的规则性及其边界性质[J].河北大学学报（自然科学版）,1990,10(2):1-9.
2宋仁明.一类半线性方程的Dirichlet问题[J].应用概率统计,1989,5(1):61-70.
3金永阳.一类带奇异低阶项椭圆型方程的正则性[J].数学学报（中文版）,2003,46(1):143-152.
4金永阳,贾厚玉.一类椭圆方程解的连续性[J].应用数学,2002,15(2):52-56. 被引量：4
5吴冬生.扩散方程广义解的规则性[J].河北大学学报（自然科学版）,1994,14(3):8-12.
6蹇素雯,杨凤藻.奇异半线性抛物方程初值问题解的存在性与不存在性,Blow-up问题及解的无限增长性[J].数学物理学报（A辑）,1997,17(4):439-446. 被引量：13
7李书菊,杨凤藻.奇异半线性抛物方程的Cauchy问题研究[J].云南民族大学学报（自然科学版）,2006,15(3):185-188.
8林荣斐,吕杰林.一类次椭圆方程弱解的正则性[J].应用泛函分析学报,2009,11(4):314-317.
9陈传钟,孙玮.非对称Dirichlet型的扰动及其结合的Markov过程[J].数学物理学报（A辑）,2001,21(2):145-153. 被引量：3
10李芳芳,张松艳.非齐次散度型椭圆方程的正则性[J].宁波大学学报（理工版）,2011,24(3):45-47.

Chinese Quarterly Journal of Mathematics

2002年第1期

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Singular Solutions of the Cauchy Problem for SemilinearParabolic Equations with Singular Potentions

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