半线性抛物型方程定义的光滑强单调流收敛于半渐近稳定的奇点

Colnergence to Semi-Asymptotically Stable Eqtiilibria in Smooth Strongly Mono-tone Flows Defined by Semi-linear Parabolic Eqtiations

本文研究半线性抛物型方程定义的光滑强单调流的渐近性态，我们给出了具有有界轨线且不收敛于半渐近稳定奇点的点集在Ｘ￣α中是第一范畴的充要条件，我们还研究了全有序奇点弧的存在性和非平凡不变函数的存在性之间的等价关系。

In this paper,we study the asymptotic behavior of the smooth strongly monotonefiows defined by semilinear parabolic equations.we give t he necessary and sufficient condi- tion that the set of all points whose trajectories are bounded and don’t converge to semi-asymptotically stable equilibria is meager in X￣α In addition,we investigate the relation betweenthe existence of simply ordered are consisting of equilibria and the existence of nonconstant in- variant function.