带有点源和非局部边界条件的多孔介质方程解的爆破
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摘要
研究了一类带有点源和非局部边界条件的多孔介质方程非负解的爆破现象.运用经典的上、下解方法,并通过比较原理,在不同的假设下,构造出了方程合适的上解或下解,得出了该方程解的整体存在性和在有限时间爆破的充分条件.
In this paper,the authors investigate the blowup properties of the non-negative solutions to a porous medium equation with localized source and nonlocal boundary condition.Using the classical super and sub solution method and the comparison principle and constructing the appropriate super or sub solutions for the equation under different hypotheses,the sufficient conditions for the global existence and finite time blowup of the solution are obtained.
In this paper,the authors investigate the blowup properties of the non-negative solutions to a porous medium equation with localized source and nonlocal boundary condition.Using the classical super and sub solution method and the comparison principle and constructing the appropriate super or sub solutions for the equation under different hypotheses,the sufficient conditions for the global existence and finite time blowup of the solution are obtained.
引文
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[2]DIAZ J I.On a Nonlinear Degenerate Parabolic Equation in Infiltration or Evaporation Through a Porous Medium[J].JDiffer Equat,1987,69(3):368-403.
[3]ANDERSON J R.Local Existence and Uniqueness of Solutions of Degenerate Parabolic Equations[J].Comm Part DifferEquat,1991,16(1):105-143.
[4]DU Li-li,XIANG Zhao-yin.A Further Blow-Up Analysis for a Localized Porous Medium Equation[J].App MathComptu,2006,179(1):200-208.
[5]LIU Qi-lin,LI Yu-xiang,GAO Hong-jun.Uniform Blow-Up Rate for Diffusion Equations with Localized NonlinearSource[J].J Math Anal Appl,2006,320(2):771-778.
[6]李中平,王雄瑞,周军.一类带有局部化源的反应扩散方程组解的整体存在性及爆破[J].西南师范大学学报:自然科学版,2007,32(3):15-18.
[7]FRIEDMAN A.Monotonic Decay of Solutions of Parabolic Equations with Nonlocal Boundary Conditions[J].QuartAppl Math,1986,44(3):401-407.
[8]SEO S.Global Existence and Decreasing Property of Boundary Values of Solutions to Parabolic Equations with NonlocalBoundary Conditions[J].Paci J Math,2000,193(1):219-226.
[9]SOUPLET P.Blow-Up in Non-Local Reaction-Diffusion Equations[J].SIAM J Math Anal,1998,29(6):1301-1334.
[10]WANG Yu-lan,MU Chun-lai,XIANG Zhao-yin.Blowup of Solutions to a Porous Medium Equation with NonlocalBoundary Condition[J].Appl Math Comptu,2007,192(2):579-585.
[11]DENG K.Comparision Principle for Some Nonlinear Problems[J].Quart Appl Math,1992,50(3):517-522.