The Mathematical Institute, University of Oxford, Eprints Archive

Stability of patterns with arbitrary period for a Ginzburg-Landau equation with a mean field

Norbury, John and Wei, J. and Winter, M. (2007) Stability of patterns with arbitrary period for a Ginzburg-Landau equation with a mean field. European Journal of Applied Mathematics, 18 . pp. 129-151. ISSN 0956-7925

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Abstract

We consider a particular system of equations.
This system plays an important role as a Ginzburg-Landau equation with a mean field in several areas of the applied sciences and the steady-states of this system extend to periodic steady-states with period L on the real line which are observed in experiments. Our approach is by combining methods of nonlinear functional analysis such as nonlocal eigenvalue problems and the variational characterization of eigenvalues with Jacobi elliptic integrals. This enables us to give a complete classification of all stable steady-states for any positive $L$.

Item Type:Article
Subjects:D - G > Functional analysis
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:649
Deposited By:Richard Booth
Deposited On:12 Sep 2007
Last Modified:20 Jul 2009 14:23

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