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非局部退化拟线性抛物型方程组解的爆破和整体存在性 被引量：5

Blow-up and Global Existence for a Nonlocal Degenerate Quasilinear Parabolic System
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摘要 该文采用弱上下解方法和正则化技巧,研究了一类非局部退化抛物型方程组解的爆破和整体存在性,给出了爆破指标,并对非退化情形m=n=1,p_1=q_1=0,p_2q_2>1给出了一致爆破速率. This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system.The sub-and-super solutions method and the regularization skill are used.The critical exponent of the system is gained.Furthermore, for the special case m = n = 1,p1 = q1 =0,p2q21,the uniform blow-up profile is gained.
作者 陈玉娟
机构地区 东南大学数学系 南通大学理学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2010年第2期386-396,共11页 Acta Mathematica Scientia
基金 国家自然科学基金(10671210) 江苏省教育厅自然科学指导性计划项目(07KJD110166) 江苏省青蓝工程以及南通大学立项资助项目(06Z011 08B02)资助
关键词 退化抛物型方程组 非局部源 爆破 整体存在性 Degenerate parabolic system Nonlocal source Global existence Blow-up
分类号 O175.26 [理学—基础数学]
  • 相关文献

参考文献15

  • 1Anderson J R. Local existence and uniqueness of solutions of degenerate parabolic equations. Comm Patial Differential Equations, 1991, 16:105-143.
  • 2陈玉娟.非局部的退化抛物型方程组的解的爆破和整体存在性[J].数学物理学报（A辑）,2006,26(5):731-740. 被引量：6
  • 3Deng W B, Duan Z W, Xie C H. The blow-up rate for a degenerate parabolic equation with a non-local source. J Math Anal Appl, 2001, 264:577-597.
  • 4Deng W B, Li Y X, Xie C H. Blow-up and global existence for a nonlocal degenerate parabolic system. J Math Anal Appl, 2003, 277:199-217.
  • 5Deng K, Wang M K, Levine H A. The influence of nonlocal nonlinearities on the long time behavior of solutions of Burgers equation. Quart Appl Math, 1992, 50:173-200.
  • 6Escobedo M, Herrero M A. A semilinear parabolic system in a bounded domain. Ann Mat Pura Appl, 1993, CLSX(4): 307-315.
  • 7Furter J, Grinfeld M. Local vs non-local interactions in population dynamics. J Math Biology, 1989, 27: 65-80.
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二级参考文献15

  • 1Galaktionov V A, Levine H A. A general approach to critical Fujita exponents in nonlineetr parabolic problems. Nonlinear Anal, 1998, 34:1005-1027
  • 2Deng W B, Duan Z W, Xie C H. The blow-up rate for a degenerate parabolic equation with a nonlocal source. J Math Anal Appl, 2001, 264:577-597
  • 3Ph Souplet. Blow-up in nonlocal reaction-diffusion equations. SIAM Math Anal, 1998, 29:1301-1334
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  • 5Furter J, Grinfeld, Local vs. Nonlocal interactions in population dynamics. J Math Biology, 1989, 27:65-80
  • 6Deng W B, Li Y X, Xie C H. Blow-up and global existence for a nonlocal degenerate parabolic system. J Math Anal Appl, 2003, 277:199-217
  • 7Anderson J R. Local existence and uniqueness of solutions of degenerate parabolic equations. Comm Patial Differential Equations, 1991, 16:105-143
  • 8Escobedo M, Herrero M A. A semilinear parabolic system in a bounded domain. Ann Mat Pura Appl,1993, 165:307-315
  • 9Galaktionov V A, Sp.Kurdyumov, Samarskii A A. A parabolic system of quasi-linear equations Ⅱ. Differential Equations, 1983, 19:1558-1571
  • 10Deng K, Wang M K, Levine H A. The influence of nonlocal nonlinearities on the long time behavior of solutions of Burgers equation. Quart Appl Math, 1992, 50:173-200

共引文献5

同被引文献21

  • 1李梅,谢春红.退化的抛物方程组解的全局存在及爆破(英文)[J].数学杂志,2004,24(2):197-203. 被引量：6
  • 2李慧玲.一个非线性抛物型方程正解的性质[J].中国科学（A辑）,2007,37(3):257-273. 被引量：7
  • 3Fujita H. On the blowing up of solution of the cauchy problem for u, = Au + ul+~[ J ]. Fac Sci, Univ Tokyo Sect I, 1966,13:109- 124.
  • 4WU Chunchen. Blow-up and global existence for a quasilinear parabolic system [ J ]. Discrete Dynamics in Nature and Society, 2014(2014) :1- 4.
  • 5Escobedo M, Herrero M A. Boundness and blow-up for a semilinear reaction-diffusion systems [ J ]. Journal of Dynamics and Differential Equations, 1991,89 : 176-202.
  • 6Chlebik M, Fila M. From critical exponents to blow-up rates for parabolic problems [ J ]. Rendieonti Di Matematiea e Delle Sue Aoolieazioni. 1999.19 ( 4 ) :449- 470.
  • 7WU Chunchen. Blow-up and global existence for a quasilinear parabolic system [ EB/OL ]. Discrete Dynamics in Nature and Society ,2014(2014-O2-13 ) [ 2014-04-15 ]. http ://www. hindawi, com/jourhals/ddns/2014/821503/.
  • 8Floater M S, Mcleod J B. Blow-up at the boundary for degenerate semilinear parabolic Equations [ J ]. Arch Rational Mech Anal, 1991 (114) :57-77.
  • 9CHEN You peng,LIU Li hua.Global blow-up for a localized nonlinear parabolic equation with a nonlocal boundary condition[J].J Math Anal Apple,2011,38(4):421-430.
  • 10COURANT R,Hilbert D.Methods of Mathematical Physics II[M].New York:Interscience,1962.

引证文献5

二级引证文献4

数学物理学报（A辑）
2010年 第2期

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