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一类具有非齐次边界条件的非线性抛物方程解的梯度爆破问题 被引量：1

Gradient Blow-up Problem for a Nonlinear Parabolic Equation with Nonhomogeneous Boundary Condition
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摘要 讨论了如下一类带有齐次边界条件的非线性抛物方程ut-△u=|u|p+a(x)uq解的爆破问题,给出了方程解梯度爆破和L∞爆破的条件. The following nonlinear parabolic equation with nonhomogeneous boundary data ut-△u=｜△↑u｜^p＋α（x）u^qis studied. And the gradient blow-up and L^∞ blow-up conditions of the solution are obtained.
作者 刘浏
机构地区 达县师范高等专科学校数学系
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2005年第5期885-888,共4页 Journal of Sichuan University(Natural Science Edition)
关键词 非线性抛物方程 非齐次边界条件 梯度爆破 L^∞爆破 nonlinear parabolic equation nonhomogeneous boundary gradient blow-up L^∞ blow-up
分类号 O175.26 [理学—基础数学]
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参考文献3

  • 1Souplet P. Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions[J]. Diff.Integral Equations, 2002, 15: 237 - 256.
  • 2Alaa N, Pierre M. Weak solutions of some quasilinear elliptic equations with data measures[J]. SIAM J. Math. Anal,1993, 24:23-25.
  • 3Evans C.Partial differential equations[M].Rhode Island:AMS Providence,1998.

同被引文献12

  • 1Z. Wu, J. Zhao, J. Yin, et al. Nonlinear Diffusion Equation[M]. River Edge, N J: World Scientific Publishing Co. Inc., 2001.
  • 2O. A. Ladyzhenskaia, V. A. Solonnikov, N. N. Uralceva. Linear and Quasilinear Equations of Parabolic Type[M]. Providence, RI: Amer. Math. Soc. Translations, 1967.
  • 3A. Friedman. Partial Differential Equations of Parabolic Type[M]. Englewood Cliffs, N. J.: Prentice-Hall Inc., 1964.
  • 4Souplet, Philippe. Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions[J]. Differential Intergral Equations, 2002, 15(2): 237-256.
  • 5J. Ball. Remarks on blow-up and nonexistence theorems for nonlinear evolution equations[J]. Quart. J. Math. Oxford ser.(2), 1977, 28(112): 473-486.
  • 6Murray H. Protter, Hans F. Weinberger. Maximum Principles in Differential Equations[M]. New York: Springer-Verlag, 1967.
  • 7S. Angenent, M. Fila. Interior gradient blow-up in a semilenear parabolic equation[J]. Diff. Intergral Equations, 1996, 9: 865- 877.
  • 8K. Asai, N. Ishimura. On the interior derivative blow-up for the curvature evolution of capillary surfaces[J]. Proc. Amer. Math. Soc., 1998, 126: 835-840.
  • 9T. Dlotk. Examples of parabolic problems with blowing-up derivatives[J]. J. Math. Anal. Appl., 1991, 1554: 226-237.
  • 10M. Fila, G. Lieberman. Derivative blow-up and beyond for quasilinear parabolic equations[J]. Diff. Intergral Equations, 1994, 7: 811-821.

引证文献1

四川大学学报（自然科学版）
2005年 第5期

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