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一类退化抛物方程解的存在唯一性及爆破速率 被引量：11

Existence and Uniqueness and Blow up Rate of Solutions for Degenerate Parabolic Equations
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摘要 本文运用正则化方法证明了一类退化抛物方程解的存在唯一性,讨论了解的全局存在性与爆破,并在一定的初值条件下得到了解的爆破速率. In this paper, we establish the local existence and uniqueness of the solution by using regularization method. We also obtain the global existence and nonexistence. Finally, we get the blow-up rate.
作者 刘其林 邓卫兵 谢春红
机构地区 东南大学数学系 南京大学数学系
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2003年第4期775-784,共10页 Acta Mathematica Sinica：Chinese Series
关键词 退化抛物方程 爆破 爆破速率 Degenerate parabolic equation Blow-up Blow-up rate
分类号 O175.26 [理学—基础数学]
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参考文献5

  • 1Ph. Souplet, Blow up in nonlocal reaction-diffusion equations, SIAM J. Math. Anal., 1998, 29: 1301-1334.
  • 2Ph. Souplet, Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source, J. Diff. Eqns., 1999, 153: 374-406.
  • 3Wang M. X.I Wang Y. M., Properties of Positive solutions for nonlocal reaction-diffusion problems, Math.Meth. Appl. Sic., 1996, 19: 1141-1156.
  • 4Anderson J. R., Local existence and uniqueness of solutions of degenerate parabolic equations, Comm. Partial Differential Equations, 1991, 16: 105-143.
  • 5Aronson D. G., Grandall M. G., Peletier L. A., Stabilization of solutions of a degenerate nonlinear diffusion problem, J. Nonlinear Anal. Theory Method Appl., 1982, 6: 1001-1022.

同被引文献86

  • 1孔令花,王明新.带有非局部源和非局部边界条件的抛物型方程组解的爆破性质[J].中国科学（A辑）,2007,37(7):817-832. 被引量：10
  • 2Wang M, Wang Y. Properties of positive solutions for non-local reaction-diffusion problems[ J ]. Mathematical Methods in the Applied Sciences, 1996, 19:1141-1156.
  • 3Souplet Ph. Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear soruce[ J]. Journal of Differential Equations, 1999, 153 : 374 -406.
  • 4J. von Below, G. Pincer Mailly. Blow up for reaction diffusion equations under dynamical boundary conditions[ J]. Comm. Partial Differential Equations, 2003, 28 : 269 - 298.
  • 5Gagelle Pincet Mailly. Blow up for nonlinear parabolic equations with time degeneracy under dynamical boundary conditions[ J]. Journal of Nonlinear Analysis, 2007, 67 : 657 - 667.
  • 6Ph.Souplet,Uniform blow-up profiles and boundary behavior for diffusion equations with non-local nonlinear source[J].J.Diff.Eqns.1999,153:374-406.
  • 7C.V.Pao,Nonlinear Parabolic and Elliptic Equations[M].Plenum Press,New York,1992.
  • 8Ph.Souplet,Blow up in non-local reaction-diffusion equations[J].SIAM Y.Math.Anal.1998,29(6):1301-1334.
  • 9A.Friedman,J.B.Mcleod,Blow-up of solutions of non-linear degenerate parabolic equations[J].Arch.Rat.Mech.Anal.1986,96:55-80.
  • 10Z.W.Duan,W.B.Deng & C.H.Xie,Uniform blow-up profile for a degenerate parabolic system with nonlocal source[J].Computers and Mathematics with Applications,2004,47:977-995.

引证文献11

二级引证文献11

数学学报（中文版）
2003年 第4期

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