一类反应扩散方程的分歧分析

文章讨论了一类反应扩散方程的分歧（分岔）现象。运用所谓基于Ｌ－Ｓ（李雅普诺夫－施密特）约化的奇异理论方法，得到了满意的结果。  

定常Kuramoto-Sivashinsky方程关于非线性伽辽金方法的一个注记

本文讨论了定常Ｋ－Ｓ方程关于伽辽金方法和非线性伽辽金方法的收敛性和最大模估计；对相同模数而言，两者的误差阶完全一致，数值结果表明非线性伽辽金方法同样成功地计算出了Ｋ－Ｓ方程的分歧解，并且在计算时间方面非线性伽辽金方法比伽辽金方法要少得多。  

关于u″＋μ（u—u^k）=0（4≤k∈Z^＋）分叉的注记

讨论了一类反应扩散方程ｕ＋μ（ｕ－ｕ＾ｋ）＝０，ｕ（０）＝ｕ（π）＝０的分叉现象，运用所谓基于李雅普诺夫－施密特约化的奇异理论方法，得到满意的结果。  

圆截面弯管流动的数值研究

本文利用有限差分方法研究稍微有点弯曲的圆截面管道中粘性流体的稳定流动,数值结果表明我们所取的算法是合理的和有效的。  

二维Kuramoto—Sivashinsky方程的非平凡分歧解及其稳定性

这篇文章讨论了二维K-S方程的分歧现象。对于给定的正整数n_0,m_0,a=n_0~2 m_0~2是一个分歧点,在a附近从平凡解分歧出来的非平凡解枝数依赖于不定方程n~2 m~2=a解的个数,本文给出了解的渐近表示,并讨论了它们的稳定性。  

ERROR ESTIMATES OF GALERKIN METHOD FOR HIGH DIMENSIONAL STEADY STATE KURAMOTO-SIVASHINSKY EQUATION

1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｐｅｒ,ｗｅｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇＫ -Ｓｅｑｕａｔｉｏｎ (ｆｏｒｅｘａｍｐｌｅ,ｓｅｅ [1 ] -[3]ａｎｄｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ)ｉｎｓｐａｃｅｄｉｍｅｎｓｉｏｎ≥ 3:Δ2 ｕ+Δｕ+ 12 ｜ ｕ｜2 -12 Ｎｉ=1ｌｉ∫ＩＮ｜ ｕ｜2 ｄｘ=0 ,ｘ∈ＩＮ,(1 )ｗｉｔｈＬ ｐｅｒｉｏｄｉｃｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｓ,Ｌ =(ｌ1,ｌ2 ,… ,ｌＮ)ｂｅｉｎｇｔｈｅｓｉｚｅｏｆａｔｙｐｉｃａｌｐａｔｔｅｒｎｃｅｌｌ (ａｌｓｏｂｉｆｕｒｃａｔｉｏｎｐａｒ…  

REMARK ON GALERKIN METHOD FOR TWO-DIMENSIONAL STEADY STATE KURAMOTO-SIVASHINSKY EQUATION

1　IntroductionThe K-S equation represents a class of pattern formation equations.It has beenstudied extensively in recent years,both in the context of inertial manifolds and finite-di-mensional attractors as well as in numerical simulations of system dynamical behaviour( see[2 ,4 ,7-1 0 ] ) .Despite many studies of dynamical behaviour of the K_ Sequation,the steady-state analysis of the equation has not been thoroughly carried out,which ispractically important and theoretically interesting.…  

关于K-S方程的非线性伽辽金方法(英文)

该文讨论了关于 K- S方程的伽辽金方法和非线性伽辽金方法的收敛性和 L2 误差估计 ,并得出误差阶一致的结论  

REMARKS ON BIFURCATIONS OF u" μu-u~κ=0(4≤k∈Z~ )

1. IntroductionOne class of reaction-diffusion equations in one-spatial dimension reads as [1,2],where p is a parameter, 1 < k E Z .Li has ever considered the static (or steady-stste) bifurcations of (4) for the simplercases with k = 2, 3 in [3]. In this paper, we focus on studying the static bifurcations of (4)for the complicated cases with 4 5 k E Z . That is, we consider the bifurcations of thefollowing equationwhere p is a parameter and 4 5 k E Z .Let X = {u E C'[0,7] I u(0) ~ u(x) = …