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一类具有非线性记忆的半线性抛物方程解的爆破速率 被引量：1

Blow-up rate of the solution for a class of semilinear parabolic equation with nonlinear memory
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摘要 作者研究了如下的具有齐次Dirichlet边界的半线性抛物方程:u_t—Δu=integral from n=0 to t (m(t-τ)f(u(x,τ))dr+u(x,t)),x∈Ω,t>0,并得到其解在有限时间爆破的条件以及爆破速率的估计。 The following semilinear parabolic equation：ut-△u=∫0^t m（t-τ）f（u（x,τ））dτ＋u（x,t）,x∈Ω,t〉0.with homogeneous Dirichlet boundary boundary condition is studied, and the finite time blow-up condition and the blow-up rate estimate are obtained.
作者 吕峰 樊明书 徐思
机构地区 四川大学数学学院 四川大学锦城学院数学教研室 江西财经职业学院数学系
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2009年第1期29-32,共4页 Journal of Sichuan University(Natural Science Edition)
关键词 半线性抛物方程 非线性记忆 爆破速率 Semilinear parabolic equation, nonlinear memory, blow-up rate
分类号 O175.26 [理学—基础数学]
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参考文献9

  • 1Pao C V. Nonlinear parabolic and elliptic equations[M]. New York: Springer, 1992.
  • 2Bellout H. Blow-up of solutions of parabolic equatons with nonlinear memory[J]. J Diff Eq, 1987, 70: 42.
  • 3Li Y X, Xie C H. Blow-up for semilinear parabolic equations with nonlinear memory[J]. Z Angew Math Phys, 2004, 55: 15.
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  • 8Komkov V. Continuability and estimates of solutions of (α(t)φ(x)x')'+c(t)f(x)=0[J]. Ann Polon Math, 1974, 30: 125.
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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）
2009年 第1期

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