Chinese Quarterly Journal of Mathematics ›› 2002, Vol. 16 ›› Issue (1): 1-8.

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Singular Solutions of the Cauchy Problem for Semilinear Parabolic Equations with Singular Potentions 

  

  1.  中国科学技术大学数学系中国科学技术大学数学系 安徽合肥230026 
  • Received:1999-07-08 Online:2002-03-30 Published:2024-05-10
  • About author:ZENG You-dong(1961-),male,native of Yushan,Jiangxi,Ph.D.,an associate professor of University of Science and Technology of China,engages in nonlinear partial differential equations.
  • Supported by:
    Supported by the National Natural Science Foundation of China(10071080);Supported by the Fund of
    Education Ministry

Abstract: 本文研究奇异半线性抛物方程ut-Δu+V1(x)u =V2 (x)up,x ∈Rn\{ 0 } ,t>0 的Cauchy问题解的存在性。这里 ,V1(x) ,V2 (x)可以在原点具有奇性。利用Kato类函数和Greentight函数及不动点定理证明了问题存在正的奇异解 ,它在原点具有奇性 .

Key words: 奇性, Kato类, Greentight函数, 不动点,  ,

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