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November  2001, 1(4): 527-541. doi: 10.3934/dcdsb.2001.1.527

The stochastic Landau equation as an amplitude equation

D. Blömker 1, , S. Maier-Paape 1, and  G. Schneider 2,

1. 

Institut für Mathematik, RWTH Aachen, D-52062 Aachen, Germany, Germany
2. 

Mathematisches Institute, Universität Bayreuth, D-95440 Bayreuth, Germany

Received  February 2001 Revised  May 2001 Published  September 2001

We consider a stochastic partial differential equation (Swift-Hohenberg equation) on the real axis with periodic boundary conditions that arises in pattern formation. If the trivial solution is near criticality, and if the stochastic forcing and the deterministic (in)stability are of a comparable magnitude, a so called stochastic Landau equation can be derived in order to describe the dynamics of the bifurcating solutions. Here we establish attractivity and approximation results for this equation.
Keywords: stochastic amplitude equation, Landau equation., Swift-Hohenberg equation.
Mathematics Subject Classification: 60H15, 60H1.
Citation: D. Blömker, S. Maier-Paape, G. Schneider. The stochastic Landau equation as an amplitude equation. Discrete and Continuous Dynamical Systems - B, 2001, 1 (4) : 527-541. doi: 10.3934/dcdsb.2001.1.527
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