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一类含非局部源的非线性退化扩散方程解的爆破性质

邓卫兵 刘其林 谢春红

邓卫兵, 刘其林, 谢春红. 一类含非局部源的非线性退化扩散方程解的爆破性质[J]. 应用数学和力学, 2003, 24(11): 1204-1210.
引用本文: 邓卫兵, 刘其林, 谢春红. 一类含非局部源的非线性退化扩散方程解的爆破性质[J]. 应用数学和力学, 2003, 24(11): 1204-1210.
DENG Wei-bing, LIU Qi-lin, XIE Chun-hong. The Blowup Properties for a Class of Nonlinear Degenerate Diffusion Equation With Nonlocal Source[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1204-1210.
Citation: DENG Wei-bing, LIU Qi-lin, XIE Chun-hong. The Blowup Properties for a Class of Nonlinear Degenerate Diffusion Equation With Nonlocal Source[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1204-1210.

一类含非局部源的非线性退化扩散方程解的爆破性质

详细信息
    作者简介:

    邓卫兵(1971- ),男,江苏人,讲师,博士(E-mail:wbdeng@nju.edu.cn).

  • 中图分类号: O175.26

The Blowup Properties for a Class of Nonlinear Degenerate Diffusion Equation With Nonlocal Source

  • 摘要: 研究了一类带非局部源的非线性退化抛物型方程.在一定条件下,证得方程的解在有限时刻爆破且爆破点集为整个区域.积分方法被用来研究解的爆破性质.
  • [1] Cantrell R S,Consner C.Diffusive logistic equations with indefinite weights:population models in disrupted environments Ⅱ[J].SIAM J Math Anal,1991,22(4):1043-1064.
    [2] Diaz J I,Kersner R.On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium[J].J Differential Equations,1987,69(3):368-403.
    [3] Anderson J R,Deng K.Global existence for degenerate parabolic equations with a non-local forcing[J].Math Mech A ppl Sci,1997,20(13):1069-1087.
    [4] Furter J,Grinfeld M.Local vs.non-local interactions in population dynamics[J].J Math Biology,1989,27(1):65-80.
    [5] Chadam J M,Peirce A,Yin H M.The blow-up property of solutions to some diffusion equations withlocalized nonlinear reactions[J].J Math Anal Appl,1992,169(2):313-328.
    [6] Souplet Ph.Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source[J].J Differential Equations,1999,153(2):374-406.
    [7] Souplet Ph.Blow up in nonlocal reaction-diffnson equations[J].SLAM J Math Anal,1998,29(6):1301-1334.
    [8] WANG Ming-xin,WANG Yuan-ming.Properties of positive solutions for non-local reaction-diffusion problems[J].Math Mecth Appl Sci,1996,19(4):1141-1156.
    [9] WANG Shu,WANG Ming-xin,XIE Chun-hong.Nonlinear degenerate diffusion equation not in divergence form[J].Z Angew Math Phys,2000,51(1):149-159.
    [10] Friedman A,McLeod B.Blow-up of solutions of nonlinear degenerate parabolic equations[J].ArchRational Mech Anal,1987,96(1):55-80.
    [11] Anderson J R.Local existence and uniqueness of solutions of degenerate parabolic equations[J].Commun Partial Differential Equations,1991,16(1):105-143.
    [12] Pao C V.Nonlinear Parabolic and Elliptic Equations[M].New York:Plenum Press,1992.
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出版历程
  • 收稿日期:  2001-10-26
  • 修回日期:  2003-06-09
  • 刊出日期:  2003-11-15

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