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The stochastic Landau equation as an amplitude equation

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  • 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.
    Mathematics Subject Classification: 60H15, 60H10.

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