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ＣＯＭＰＬＥＸＩＴＹ ＯＦ ＬＡＲＧＥ ＴＩＭＥ ＢＥＨＡＶＩＯＵＲ ＯＦＥＶＯＬＵＴＩＯＮ ＥＱＵＡＴＩＯＮＳ ＷＩＴＨ ＢＯＵＮＤＥＤ ＤＡＴＡ 被引量：3

COMPLEXITY OF LARGE TIME BEHAVIOUR OF EVOLUTION EQUATIONS WITH BOUNDED DATA
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摘要 The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occur and the general asymptotic behaviour is complex. This behaviour reflects for large times, even on compact sets, the complexity of the initial data at infinity.
作者 J.L.VZQUEZ E.ZUAZUA
机构地区 Departamento de Matematicas
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2002年第2期293-310,共18页 数学年刊（B辑英文版）
关键词 Asymptotic behaviour SCALING Omega-limit Heat equation Hyperbolic conservation laws 复杂性 大时间行为 发展方程 有界数据 热方程 Omega极限 双曲守恒定律 半群 收敛性
分类号 O175.26 [理学—基础数学]
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参考文献34

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同被引文献24

  • 1Thierry Cazenave,Flávio Dickstein,Fred B. Weissler.Nonparabolic Asymptotic Limits of Solutions of the Heat Equation on $${\mathbb{R}}^N$$[J]. Journal of Dynamics and Differential Equations . 2007 (3)
  • 2J. A. Carrillo,J. L. Vázquez.Asymptotic Complexity in Filtration Equations[J]. Journal of Evolution Equations . 2007 (3)
  • 3Juan Luis Vázquez.Asymptotic behaviour for the porous medium equation posed in the whole space[J]. Journal of Evolution Equations . 2003 (1)
  • 4S. Kamin,L. A. Peletier.Large time behaviour of solutions of the porous media equation with absorption[J]. Israel Journal of Mathematics . 1986 (2)
  • 5S. Kamenomostskaya.The asymptotic behaviour of the solution of the filtration equation[J]. Israel Journal of Mathematics . 1973 (1)
  • 6Lee Ki,Petrosyan A,Vazquez J L.Large-time geometric properties of solutions of the evolution p-Laplacian equation. J Differ Equs . 2006
  • 7V′azquez J L.The Porous Medium Equation, Mathematical Theory. Oxford Mathematical Monographs . 2007
  • 8Wu Z Q,Yin J X,Li H L,Zhao J N.Nonlinear Diffusion Equations. . 2001
  • 9Yin J X,Wang L W,Huang R.Complexity of asymptotic behavior of the porous medium equation in R N. . 2009
  • 10Bertsch M,Kersner R,Peletier L A.Positivity versus localization in degenerate diffusion equations. Non- linear Anal TMA . 1985

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Chinese Annals of Mathematics,Series B
2002年 第2期

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