The stochastic Landau equation as an amplitude equation

D. Blömker; S. Maier-Paape; G. Schneider

doi:10.3934/dcdsb.2001.1.527

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2001, Volume 1, Issue 4: 527-541. Doi: 10.3934/dcdsb.2001.1.527

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The stochastic Landau equation as an amplitude equation

1.
Institut für Mathematik, RWTH Aachen, D-52062 Aachen
2.
Mathematisches Institute, Universität Bayreuth, D-95440 Bayreuth

Received: January 31, 2001

Revised: April 30, 2001

Published: October 2001

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Abstract

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.

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Mathematics Subject Classification: 60H15, 60H10.

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