Blow-up Problems for a Class of Semilinear Parabolic Equations

张杰明

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Blow-up Problems for a Class of Semilinear Parabolic Equations

更新时间：2026-09-14

- Blow-up Problems for a Class of Semilinear Parabolic Equations
- 一类半线性抛物型方程的爆破问题
- Issue 5, Pages: 392-393(2003)
- 作者机构：
  
  山西大学商务学院基础部,山西,太原,030006
- 作者简介：
- 基金信息：
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- Published：2003
- 稿件说明：
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张杰明. Blow-up Problems for a Class of Semilinear Parabolic Equations[J]. 2003, (5): 392-393.
DOI：

张杰明. Blow-up Problems for a Class of Semilinear Parabolic Equations[J]. 2003, (5): 392-393. DOI：

摘要

　运用Hopf最大值原理

讨论了一类具有Dirichlet边界条件的半线性抛物型方程解的爆破问题.获得了整体解的不存在性定理和爆破时刻的上界以及非整体解的爆破率的上估计.

Abstract

The Hopf′s maximum principle is utilized to deal with the problem on blowup of the solutions for a class of semilinear parabolic equations with Dirichlet boundary conditions. The nonexistence theorem of global solutions and the upper bound of blowup time as well as the upper estimate of the blowup rate of nonglobal solutions are obtained.

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references

　SperbRP.Growthestimatesinreaction-diffusionproblem[J].Arch.RationalMech.Anal.,1980,75:127-145.

　KohdaA.Blow-upcriteriaforsemilinearparabolicequations[J].J.Math.Anal.Appl.,2000,243:127-139.

　FriedmanA,McleodB.Blow-upofpositivesolutionsofsemilinearheatequations[J].IndianaUniv.Math.J.,1985,34:425-447.

　RamiandrisoaA.Blow-upfortwononlinearproblems[J].NonlinearAnal.TMA,2000,41:825-854.

　ProtterMH,WeinbergerHF.Maximumprinciplesindifferentialequations[M].Prentice-HallInc,1967.393

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