非线性发展方程的Hlder连续惯性流形  

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

作　　者：过榴晓[1] 徐振源[1] 张荣[1] 

机构地区：[1]江南大学理学院信息与计算科学系,无锡214122

出　　处：《系统科学与数学》2009年第12期1631-1643,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金青年科学基金(10901073);江南大学创新团队发展计划;江南大学自主科研计划资助课题

摘　　要：引入非线性发展方程的H(o|¨)lder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(o|¨)lder连续惯性流形也是有限维不变的,但光滑性减弱为H(o|¨)lder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(o|¨)lder连续惯性流形上约化为有限维常微分方程组。The HSlder 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 HSlder continuous inertial manifold proposed in this paper is still finite-dimensional positive invariant, and only Holder continuity is needed, the ＂spectral gap＂ condition can be ignored. The intersection set of a Holder 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 HSlder continuous inertial manifold.

关 键 词：Holder连续惯性流形 指数吸引子连续惯性流形 无穷维动力系统 指数吸引子. 

分 类 号：O193[理学—数学]