The time dependent amplitude equation for the Swift-Hohenberg problem
Precise estimates for the validity of the amplitude approximation for the swift-Hohenberg equation are given, in a fully time dependent framework. It is shown that small solutions of orderO(ɛ) which are modulated like stationary solutions have an evolution which is well described in the amplitude approximation for a time of orderO(ɛ-2). For the proofs, we use techniques for nonlinear semigroups and oscillatory integrals.
KeywordsNeural Network Statistical Physic Complex System Nonlinear Dynamics Stationary Solution
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