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.

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

  • Received Date: 2001-10-26
  • Rev Recd Date: 2003-06-09
  • Publish Date: 2003-11-15
  • A nonlinear degenerate parabolic equation with nonlocal source was considered. It is shown that under certain assumptions the solution of the equation blows up in finite time and the set of blow-up points is the whole region. The integral method is used to investigate the blowup properties of the solution.
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  • [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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