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一类具有非线性记忆和吸收项的半线性抛物方程解的爆破 被引量：1

Blow-up for semilinear parabolic equations with nonlinear memory and absorption
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摘要 作者考虑了具有齐次Dirichlet边界和吸收项的半线性抛物方程ut=Δu+uqt∫0upds-kum在(x,t)∈Ω×(t>0)内正解的爆破性质,并运用上下解的方法得到方程解在有限时间爆破和全局存在的条件. The blow-up property of positive solution is studied to the following semilinear parabolic equations： ut=△u＋u^q∫0^tu^pds-ku^m with homogeneous Dirichlet boundary conditions and absorption in Ω×（t〉0）. using the monotone method, the blow-up criteria and the condition of global existence are obtained
作者 石立新 程正琼
机构地区 四川大学数学学院 四川农业大学数学系
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第6期1313-1316,共4页 Journal of Sichuan University(Natural Science Edition)
关键词 半线性抛物方程 爆破 非线性记忆 semilinear parabolic equation, blow-up, nonlinear memory
分类号 O175.26 [理学—基础数学]
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参考文献7

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同被引文献15

  • 1王明新.非线性抛物型方程[M].北京:科学出版社,1997..
  • 2Chadam J M, Yin H M. An Iteration Procedure for a Class of Integrodifferential Equations of Parabolic Type [J]. Integral Equations Appl, 1989, 2(1) : 31.
  • 3Souplet P. Blow - up in Nonlocal Reaction - diffusion Equations [J]. SIAM Math Anal, 1998, 29 ( 6 ) : 1301.
  • 4Li F C, Huang S X, Xie C H. Global Existence and Blow - up of Solution to a Nonlocal Reaction - diffusion System[J]. Discrete Continu Dy- ham Systems,2003,9(6) : 1519.
  • 5Li Y X, Xie C H. Blow- up for Semilinear Parabolic Equations with Nonlinear Memory[J]. Z Angew Math Phys ,2004, 55 (1) : 15.
  • 6Liu D M, Mu C L, Ahmed I. Blow - up for a Semilinear Parabolic Equation with Nonlinear Memory and Nonlocal Nonlinear Boundary[J]. Tai- wanese Journal of Mathematics, 2013,17 (4) : 1353.
  • 7Anderson 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(4) : 759.
  • 8Deng K, Dong Z. Blow up for the Heat Equation with a General Memory Boundary Condition [J]. Communications on Pure Appl Anal,2012, 11(5) : 2147.
  • 9Anderson J R, Deng K. Global Solvability for the Porous Medium Equation with Boundary Flux Governed by Nonlinear Memory[J]. Math Anal Appl,2015, 432(2) :1183.
  • 10Deng KI Kwong M'K, Levine H A. The Influence of Nontocal Nonlinearities on the Long Time Behavior of Solutions of Burgers' equation[J]. Quart Appl Math, 1992,50(1) : 173.

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四川大学学报（自然科学版）
2008年 第6期

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