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。

An Inertial Manifold forTime-discretization With Non-Self Adjonit Operator

In this paper the existence of the inertial is the fixed point of the inertial map, is proved Under the assumption that h is small enough and the spectral gap conditions are satisfied for the time-discrete equation F(un). It is different from the other works [1,2] that the capter operator A in this paper is only an infinitesimal generator of an analytic semigroup and has compact resolvent without the assumption of self-adjoint.