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非线性发展方程混合问题解的爆破性质 被引量：1

Blow up Property of Solutions to the Mixed Problem of Nonlinear Evolution Equations
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摘要 讨论了具有第三类非线性边界条件的非线性发展方程的混合问题,并在已知函数满足某些假设的条件下,利用抛物型方程的最大值原理和凸性方法,证明了该问题的解在有限时间内爆破. The mixed problem with nonlinear boundary condition of the third type for nonlinear evolution equations is discussed. The blow up of solutions in a finite time is proved under some assumptions on known functions by the maximum principle and the convex method of parabolic equation.
作者 查中伟 向以华
机构地区 重庆三峡学院数学与统计学院
出处 《数学年刊（A辑）》 CSCD 北大核心 2012年第3期383-388,共6页 Chinese Annals of Mathematics
基金 重庆市科委科研基金(No.07EA7036)资助的项目
关键词 非线性发展方程 第三类边界条件 解的爆破 凸性方法 Nonlinear evolution equation, Boundary condition of the thirdtype, Blow up of solution, Convex method
分类号 O175.29 [理学—基础数学]
  • 相关文献

参考文献12

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二级参考文献28

  • 1查中伟.拟线性抛物方程解的爆破性质及其应用[J].四川大学学报（自然科学版）,2006,43(4):738-743. 被引量：3
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共引文献18

同被引文献12

  • 1王建,高文杰.具非线性边值条件的发展型p-Laplace方程解在有限时刻的爆破性和有界性[J].吉林大学学报（理学版）,2005,43(4):395-401. 被引量：6
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  • 5Anderson J R, Deng K, Dong Z. Global solvability for the heat equation with boundary flux governed by nonlinear memory [J]. Quart Appl Math, 2011, 69: 759.
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  • 7Deng K, Xu M. On solutions of a singular diffusion equation [J]. Nonlinear Anal, 2000, 41 : 489.
  • 8Hu B, Yin H M. The profile near blow up time for solutions of the heat equation with a nonlinear boundary condition [J]. Trans Amer Math Soc, 1994, 346 : 117.
  • 9Souplet P. Blow-up in nonlocal reaction-diffusion e- quations [J]. SIAM J Math Anal, 1998, 29 (6) : 1301.
  • 10Deng K, Levine H A. The role of critical exponents in blow-up theorems: The sequel [J]. J Math Anal Appl, 2000, 243: 85.

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数学年刊（A辑）
2012年 第3期

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