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半线性抛物方程具有临界初值的初边值问题 被引量：1

Initial boundary value problem of semilinear parabolic equation with critical initial data
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摘要 研究半线性抛物方程ut-Δu=f(u)具有临界初始条件J(u0)=d,I(u0)<0的初边值问题。利用位势井族方法证明了:若f(u)满足假设(H),u0(x)∈H10(Ω),J(u0)=d且I(u0)<0,则此问题不存在整体解,这样就从根本上解决了这一公开问题,并从实质上补充了已有的结果。 Abstract： The initial boundary value problem of semilinear parabolic equation ut-△u=f（u） with critical initial data J（u0）=d,I（u0）〈0 is considerd. By using the theory of potential wells, it is shown that if f（u） satisfies as-sumption （H） , u0（x）∈H0^1（Ω）,J（u0）=d and,I（u0）〈0 ,then the problem does not admit any global solution. So this open problem is resolved and the existing results are supplemented in essential.
作者 张文颖
机构地区 哈尔滨工程大学理学院
出处 《黑龙江大学自然科学学报》 CAS 北大核心 2008年第4期473-476,479,共5页 Journal of Natural Science of Heilongjiang University
基金 国家自然科学基金资助项目(10271034) 哈尔滨工程大学基础研究基金资助项目(HEUF04012)
关键词 半线性抛物方程 初边值 临界初值 位势井 整体不存在性 semilinear parabolic equations initial boundary value critical initial data potential wells global non-existence
分类号 O175.26 [理学—基础数学]
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参考文献12

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共引文献14

同被引文献26

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引证文献1

黑龙江大学自然科学学报
2008年 第4期

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