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一个带非局部源的反应扩散方程组解的存在性和渐近性态 被引量：5

Existence and Asymptotic Behavior of Solution for a Reaction Diffusion System with Nonlocal Source
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摘要 本文研究带非局部源的半线性反应扩散方程组,并通过建立比较定理,利用Schauder不动点定理证明古典解的存在唯一性,得到了解的爆破点集与解的渐近性态. Abstract In this paper, a semi-linear reaction diffusion system with nonlocal source is considered, and existence and uniqueness of the classical solution are proved by establishing a comparison theorem and employing the Schauder fixed point theorem. The blow-up set and asymptotic behavior of solution are also obtained.
作者 栗付才 谢春红
机构地区 南京大学数学系
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2002年第6期1185-1196,共12页 Acta Mathematica Sinica：Chinese Series
关键词 反应扩散方程组 存在性 非局部源 古典解 爆破点集 解 渐近性态 Nonlocal source Classical solution Blow-up set Asymptotic behavior of solution
分类号 O175.26 [理学—基础数学]
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参考文献11

  • 1Candam J. M., Peire A., Yin H. M., The Blow-up property of the solutions to some diffusion equations withlocalized nonlinear reactions, J. Math. Anal. Appl., 1992, 169(2): 313-328.
  • 2Pao C. V., Blowing-up of solution for a nonlocal reaction-diffusion problem in combustion theory, J. Math.Anal. Appl., 1992, 166(2): 591-600.
  • 3Wang M., Wang Y., Properties of positive solutions for non-local reaction-diffusion Problems, Math. Meth. Appl. Sci., 1996, 19(14): 1141-1156.
  • 4Pao C. V., Nonexitence of global solution for an integrodifferential system in reactor dynamics, SIAM J. Math. Anal., 1980, 11(3): 559-564.
  • 5Guo J. S., Su H. W., The Blow-up behavior of the solution of an integrodifferential equations, Differential Integral Equations, 1992, 5(6): 1237-1245.
  • 6Infante E. F., Walker J. A., On the stability properties of an equation arising in reactor dynamics, J. Math. Anal. Appl., 1976, 55(1): 112-124.
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  • 10Soupet P. H., Blow-up in nonlocal reaction-diffusion equations, SIAM J. Math. Anal., 1998, 29(4): 1301- 1334.

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数学学报（中文版）
2002年 第6期

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