H\"older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., Open Access Library" />
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系统科学与数学 2009
H(O)LDER CONTINUOUS INERTIAL MANIFOLD FOR NONLINEAR EVOLUTIONARY EQUATION
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Abstract:
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.