Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations

DOI10.1007/BF02108810zbMath0803.35140OpenAlexW2098631697MaRDI QIDQ1330941

Guido Schneider

Publication date: 10 August 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02108810

zbMATH Keywords

Ginzburg-Landau equationreaction-diffusion equationsattracting set of solutionsKuramoto- Shivashinsky equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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Attractivity of the Ginzburg-Landau mode distribution for a pattern forming system with marginally stable long modes, Aproximation and attractivity properties of the degenerated Ginzburg-Landau equation, Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation, Large-amplitude modulation of periodic traveling waves, Justification of the Ginzburg-Landau approximation in case of marginally stable long waves, Justification of mean-field coupled modulation equations, Traveling hole solutions of the complex Ginzburg-Landau equation: A review, The world of the complex Ginzburg-Landau equation, Null controllability of the complex Ginzburg-Landau equation, Nonlinear convective stability of travelling fronts near Turing and Hopf instabilities, Modulation equation and SPDEs on unbounded domains, The Validity of Generalized Ginzburg-Landau Equations

Cites Work

• On the abstract Cauchy problem of parabolic type in spaces of continuous functions
• The Ginzburg-Landau manifold is an attractor
• On the validity of the Ginzburg-Landau equation
• The time dependent amplitude equation for the Swift-Hohenberg problem
• The validity of modulation equations for extended systems with cubic nonlinearities
• Finite bandwidth, finite amplitude convection
• Non-linear wave-number interaction in near-critical two-dimensional flows
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