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Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation

Wayne, C. Eugene
Published in Communications in Mathematical Physics. 1997, vol. 190, no. 1, p. 173-211
Abstract In this paper we describe invariant geometrical structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally stable (i.e., the linearized problem about these states has continuous spectrum extending all the way up to zero), there exist finite dimensional invariant manifolds in the phase space of this equation which determine the long-time behavior of solutions near these stationary solutions. In particular, using this point of view, we obtain a new demonstration of Schneider's recent proof that these states are nonlinearly stable.
Keywords ManifoldPhase spaceStationary stateStability analysisPeriodic solution
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ECKMANN, Jean-Pierre, WAYNE, C. Eugene, WITTWER, Peter. Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation. In: Communications in Mathematical Physics, 1997, vol. 190, n° 1, p. 173-211. https://archive-ouverte.unige.ch/unige:109103

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Deposited on : 2018-10-12

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