The Validity of Generalized Ginzburg-Landau Equations

DOI<717::AID-MMA792>3.0.CO;2-Z 10.1002/(SICI)1099-1476(199606)19:9<717::AID-MMA792>3.0.CO;2-ZzbMath0874.35050OpenAlexW1966250520MaRDI QIDQ4882935

Guido Schneider

Publication date: 10 November 1997

Full work available at URL: https://doi.org/10.1002/(sici)1099-1476(199606)19:9<717::aid-mma792>3.0.co;2-z

zbMATH Keywords

continuous spectrumKuramoto-Sivashinsky equationcenter manifoldFourier space

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55)

Related Items (14)

Stability of Traveling Oscillating Fronts in Complex Ginzburg Landau Equations ⋮ Numerical Continuation and SPDE Stability for the 2D Cubic-Quintic Allen--Cahn Equation ⋮ Modulation equation for SPDEs in unbounded domains with space-time white noise -- linear theory ⋮ Validity of amplitude equations for nonlocal nonlinearities ⋮ Rotating spirals in oscillatory media with nonlocal interactions and their normal form ⋮ Approximate solution of the Kuramoto-Shivashinsky equation on an unbounded domain ⋮ Numerical study of amplitude equations for SPDEs with degenerate forcing ⋮ Amplitude equation for the generalized Swift-Hohenberg equation with noise ⋮ Multiscale expansion of invariant measures for SPDEs ⋮ Numerical continuation for fractional PDEs: sharp teeth and bloated snakes ⋮ The Swift-Hohenberg equation under directional-quenching: finding heteroclinic connections using spatial and spectral decompositions ⋮ Amplitude equations for SPDEs with cubic nonlinearity forced by general multiplicative Gaussian noise ⋮ Modulation equations: Stochastic bifurcation in large domains ⋮ Dominant dynamics for a class of singularly perturbed stochastic partial differential equations with quadratic nonlinearities and random Neumann boundary conditions

Cites Work

• Propagating fronts and the center manifold theorem
• Reduction of PDEs on domains with several unbounded directions: A first step towards modulation equations
• On nonlinear problems of mixed type: A qualitative theory using infinite- dimensional center manifolds
• The Ginzburg-Landau manifold is an attractor
• A new estimate for the Ginzburg-Landau approximation on the real axis
• On the validity of the Ginzburg-Landau equation
• Essential manifolds for an elliptic problem in an infinite strip
• Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations
• Error estimates for the Ginzburg-Landau approximation
• A center-stable manifold theorem for differential equations in Banach spaces
• The time dependent amplitude equation for the Swift-Hohenberg problem
• Analyticity of Ginzburg-Landau modes
• The validity of modulation equations for extended systems with cubic nonlinearities
• Attractors for modulation equations on unbounded domains-existence and comparison
• Finite bandwidth, finite amplitude convection
• Non-linear wave-number interaction in near-critical two-dimensional flows

This page was built for publication: The Validity of Generalized Ginzburg-Landau Equations