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一维热传导方程爆破解的数值模拟 被引量：1

Numerical Simulation of Blowup Solutions for One-dimensional Heat Conduction Equation
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摘要 本文讨论半线性抛物方程u/t=Δu,x∈Ω ,t>0,在第二类边值条件下u/n=up,x∈Ω ,t>0解的有限时间爆破问题。从一维方程出发,主要考虑一维方程的数值解问题,以及分别利用Matlab的pdepe函数和有限差分进行数值模拟。 In this paper, the finite time blowup solutions of the semilinear parabolic equation （a）u/（a）t=△u,x∈Ω,t〉0, under the second boundary condition（a）u/（a）n=up,x=（a）Ω,t〉0 were mainly discussed. Using the methods of Matlab pdepe function and finite difference respectively, we study the numerical simulation of blowup solutions for one - dimensional heat equations.
作者 贾海峰
机构地区 郑州大学数学系 郑州幼儿师范高等专科学校
出处 《长春师范学院学报（自然科学版）》 2013年第5期8-12,共5页 Journal of Changchun Teachers College
基金 国家自然科学基金资助项目(10702065)
关键词 一维 热方程 爆破 pdepe 有限差分法 数值解 One - dimensional Heat equation Blowup Pdepe Finite - difference
分类号 O175 [理学—基础数学]
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参考文献14

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同被引文献6

  • 1Polking,John.Albert,Bogges.Dave,Arnold.Differential Equations.Pren- ticeHall,2002.
  • 2Arnold,David.His matlab and LATEX expertise.
  • 3Cooper,Jeffery.Introduction to Partial Differential Equations with MATLAB.Birkhauser, 1998.
  • 4The Sauceman.His LATEX expertise.
  • 5Walter A. Strauss.Partial Differential Equations:An Introduction. John Wiley & Sons,1992.
  • 6H.A.Levine,L.E.Payne.Nonexistence theorems for the heat equ- ation with nonlinear boundary conditions and for the porous me- dium equation backward in time[J].J. Differential Equations,1974 (16):319-334.

引证文献1

二级引证文献4

长春师范学院学报（自然科学版）
2013年 第5期

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