非自治反应扩散方程的逼近惯性流形

Approximate Inertial Manifold for Nonautonomous Reaction Diffusion Equation

着重研究了具有拟周期外力的非自治反应扩散方程解的长时间性态，利用斜积流、延伸相平面法以及能量估计等方法，对非自治反应扩散方程证明了逼近惯性流形的存在性，同时构造得到一簇逼近惯性流形。

In this article, the long time behavior of nonautonomous reaction diffusion equation with quasiperiodic external force is studied. By the methods of skew-product, extended phase space and energy estimate etc, the existence of approximate inertial manifolds for nonautonomous reaction diffusion equation is proved, and the family of approximate inertial manifolds is constructed, and the sequences of such manifolds provide better approximations to the uniform attractor.