Spectral barriers and inertial manifolds for dissipative partial differential equations |
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| Authors: | P Constantin C Foias B Nicolaenko R Témam |
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| Institution: | (1) Department of Mathematics, University of Chicago, 60637 Chicago, Illinois;(2) Department of Mathematics, Indiana University, 47405 Bloomington, Indiana;(3) Los Alamos National Laboratory, Theoretical Division and Center for Nonlinear Studies, 87545 Los Alamos, New Mexico;(4) Department of Mathematics, Université de Paris-Sud, 91405 Orsay, France |
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| Abstract: | In recent years, the theory of inertial manifolds for dissipative partial differential equations has emerged as an active area of research. An inertial manifold is an invariant manifold that is finite dimensional, Lipschitz, and attracts exponentially all trajectories. In this paper, we introduce the notion of a spectral barrier for a nonlinear dissipative partial differential equation. Using this notion, we present a proof of existence of inertial manifolds that requires easily verifiable conditions, namely, the existence of large enough spectral barriers. |
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| Keywords: | Spectral barriers inertial manifolds dissipation |
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