Amplitude Equations for Locally Cubic Nonautonomous Nonlinearities

DOI10.1137/S1111111103421355zbMath1088.60062MaRDI QIDQ4441840

Dirk Blömker

Publication date: 8 January 2004

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

bifurcationpattern formationSPDEmultiple scale analysisseparation of time-scalesslow modesapproximate center-manifold

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems (37L65) Infinite-dimensional random dynamical systems; stochastic equations (37L55)

Related Items (11)

Reduced dynamics for delayed systems with harmonic or stochastic forcing ⋮ Qualitative properties of local random invariant manifolds for SPDEs with quadratic nonlinearity ⋮ Stochastic amplitude equation for the stochastic generalized Swift-Hohenberg equation ⋮ Effective splitting of invariant measures for a stochastic reaction diffusion equation with multiplicative noise ⋮ Early-warning signs for pattern-formation in stochastic partial differential equations ⋮ Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation ⋮ APPROXIMATION OF THE STOCHASTIC RAYLEIGH–BÉNARD PROBLEM NEAR THE ONSET OF CONVECTION AND RELATED PROBLEMS ⋮ Multiscale expansion of invariant measures for SPDEs ⋮ Fast-diffusion limit with large noise for systems of stochastic reaction-diffusion equations ⋮ Modulation equations: Stochastic bifurcation in large domains ⋮ Stochastic rotating waves

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