椭圆型方程伪域方法的高阶外推算法

在n维空间的有界区域Ω_1上考虑微分方程:下面的假设下讨论(1.1):     

SMOOTHNESS OF INERTIAL MANIFOLD UNDER TIME DISCRETIZATION

0IntroductionInertialmanifolds(IM)arenewobjectsthathavebeenintroducedinrelationwiththestudyoflargetimebehaviorofnonlineardissipativePDE,see[1].In[2],theyareextendedtodiscretizeddynamicsstemmingfromdissipativePDE.Frommathematicalpointofview,thesearesmootllfiniteLipschitzmanifoldsthatareinviantbytheflowofassociatedsolutions,andattractallthetrajectorieswithexponentialspeed,see[1].Fromphysicalpointofview,IMmodeltheinteractionlawsbetweensmallandlargestructureofaturbulentflow,andrepresentsitspe…     

非自伴算子时间离散化惯性流形

本文讨论了离散化方程（ｕ＾ｎ＋１－ｕ＾ｎ）／ｈ＋Ａｕ＾ｎ＋１＝Ｆ（ｕ＾ｎ）的惯性流形,证明了在ｈ充分小且算子Ａ满足谱间隔条件下,该方程存在一个惯性流形Ｍｈ＝Ｇｒａｐｈ（φｈ）,φｈ是惯性映射的不动点,与现有文献「１,２」不同,我们仅假设主算子Ａ是解析半群无空凶且有紧豫解式,不需要Ａ是自伴的假设。