(1+2)维斑图方程的动力学性态  

Dynamical behavior of the (1+2)D pattern formation

作　　者：戴正德[1] 

机构地区：[1]云南大学网络教育学院,云南昆明650091

出　　处：《云南大学学报（自然科学版）》2003年第3期181-184,共4页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金资助课题(19861004).

摘　　要：研究了在流体的有限层面由浮力或曲面张力梯度诱导的斑图构成方程,界于不良热导体平展边界间的斑图构成方程由Knobloch于1990年导出 u t=αu-μ 2u- 4u+K ·(｜ u｜2 u+β 2u u-γu u+δ ｜ u｜2),其中,u是面函数,μ是Rayleigh数,K=1,α表示热传递效益,是有限Biot数,当界面顶部和底部条件不相同时,β≠0,δ≠0,当出现非Boussinesq效应时,γ≠0,考虑α<0,μ>0,β=δ=0情形,即界面顶部和底部条件相同且出现非Boussinesq效应时(1+2)维Knobloch方程解的动力学性态,获得解的局部存在、整体存在以及吸引子的存在性.The equation of pattern formation induced by buoyancy or by surfacetension gradient in thin layer is considered,the equation confined between horizontal poor heat conductors is introduced by Knobloch (1990)ut=αu-μ2u-4u+K·(|u|2u+β2uu-γuu+δ|u|2),where u is the planform function,μ is the scaled Raifleigh number,K=1 and α represents the effects of a heat transfer finite Biot number.The β,δ and γ represent the boundary condition at top and bottom or nonBoussinesg effects respectively.The Knobloch equation with α<0,μ>0,β=δ=0(the boundary condition at top and bottom is the same) is considered,the local existence,global existence in the L2(Ω)-space and the global attractor have been obtained respectively.

关 键 词：Knobloch方程 流体 斑图方程 动力学性态 有限层面 曲面张力 不良热导体 热传递效益 吸引子 存在性 

分 类 号：O175.29[理学—数学]