非线性发展方程的H(o)lder连续惯性流形

引入非线性发展方程的H\"older连续惯性流形的概念,为原来惯性流形概念的推广和修正.惯性流形是有限维不变的Lipschiz流形,是研究发展方程解的长时间性态的合适工具,其缺点是需要谱间隙条件.提出H\"older连续惯性流形也是有限维不变的,但光滑性减弱为H\"older连续,不需要谱间隙条件.该流形与指数吸引子交集具有指数吸引性,无穷维动力系统可在H\"older连续惯性流形上约化为有限维常微分方程组.

H(O)LDER CONTINUOUS INERTIAL MANIFOLD FOR NONLINEAR EVOLUTIONARY EQUATION

The H\"older continuous inertial manifold for nonlinear evolutionary equation is introduced. Original inertial manifold is finite dimensional positive invariant Lipschitz manifold and is a convenient tool to describe a long-time behavior of dynamic system. Its' drawback is that the ``spectral gap" condition is needed. The H\"older continuous inertial manifold proposed in this paper is still finite-dimensional positive invariant, and only H\"older continuity is needed, the ``spectral gap" condition can be ignored. The intersection set of a H\"older continuous inertial manifold and an exponential attractor has exponential attraction. The infinite dimensional dynamic system can be reduced as finite dimensional ordinary differential equations on a H\"older continuous inertial manifold.