Modulation Equations: Stochastic Bifurcation in Large Domains

Abstract

We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations.

References in corpus (3)

• Formulae for the derivatives of heat semigroups
• Domain formation in transitions with noise and time-dependent bifurcation parameter
• Dynamics of defect formation

Cited by in corpus (6)

• Analysis of SPDEs arising in path sampling part II: The nonlinear case
• Numerical methods for stochastic partial differential equations with multiples scales
• Early-Warning Signs for Pattern-Formation in Stochastic Partial Differential Equations
• Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour
• Modulation equation and SPDEs on unbounded domains
• Modulation Equation for SPDEs in unbounded domains with space-time white noise -- Linear Theory