On Blow-up Problem of Solutions for a Class of Nonlinear ReacationDiffusion Equations with Mixed Boundary Conditions

张菊平; 樊志良

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On Blow-up Problem of Solutions for a Class of Nonlinear ReacationDiffusion Equations with Mixed Boundary Conditions

更新时间：2026-09-14

- On Blow-up Problem of Solutions for a Class of Nonlinear ReacationDiffusion Equations with Mixed Boundary Conditions
- 混合边界条件的非线性反应扩散方程解的Blow-up问题
- Issue 5, Pages: 313-315(2004)
- 作者机构：
  
  1. ,山西,太原,030051
  2. 华北工学院应用数学系,山西,太原,030051
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2004
- 稿件说明：
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张菊平, 樊志良. On Blow-up Problem of Solutions for a Class of Nonlinear ReacationDiffusion Equations with Mixed Boundary Conditions[J]. 2004, (5): 313-315.
DOI：

张菊平, 樊志良. On Blow-up Problem of Solutions for a Class of Nonlinear ReacationDiffusion Equations with Mixed Boundary Conditions[J]. 2004, (5): 313-315. DOI：

摘要

　利用极大值原理研究一类非线性反应扩散方程在混合边界条件下解的Blow-up问题

给出了整体解不存在的一个定理

并得到了Blow-up时间T*的上界.

Abstract

By maximum principle

the problem on blow-up of the solutions for a class of nonlinear reaction diffusion equations with mixed boundary conditions is dealt with. A nonexistence theorem of global solutions and the bound of the \!Blow-up time\" \%T\%

are obtained.

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references

　FujitaH.OntheblowingupofsolutionstotheCauchyproblemfor[J].J.FacultyScience,U.ofTokyo.,1996,13:109-124.

　SperbRP.Growthestimatesinreaction-diffusionparabolicequations[J].Comm.Pure.App.Math.,1963,16:305-330.

　LevineHA,PayneLE.Nonexistencetheoremsfortheheatequationwithnonlinearboundaryconditionandfortheporosmediumequationbackwardintime[J].J.DifferentialEquation,1974,16:319-334.

　WalterW.Onexistenceandnonexistenceinthelargeofsolutionsofparabolicdifferentialequationwithanonlinearboundarycondition[J].SIAMJ.Math.Anal.,1975,6:85-90.

　WangMX,WuYH.Globalexistenceandblow-upproblemforquasilinearparabolicequationswithnonlinearboundaryconditions[J].SIAMJ.Math.Anal.,1993,24(6):1515-1521.

　YinHM.Blow-upversusglobalsolvabiltryforaclassofnonlinearparabolicequation[J].NonlinearAnal.TMA.,1994,23(7):911-934.

　DuYH,HuangQG.Blow-upsolutionsforaclassofsemilinearellipticandparabolicequations[J].SIAMJ.Math.Anal.,31(1):1-18.

　SpervRP.Maximumprinciplesandtheirapplications[M].Academicpress.NewYork,1981,20-30.

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