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Title: Stability of patterns with arbitrary period for a Ginzburg-Landau equation with a mean field
Authors: Winter, M
Wei, J
Norbury, J
Keywords: Pattern Formation,;Mean field;Stability
Issue Date: 2007
Publisher: Cambridge University Press
Citation: European Journal of Applied Mathematics, 18(02): 129-151, Apr 2007
Abstract: We consider the following system of equations A_t= A_{xx} + A - A^3 -AB,\quad x\in R,\,t>0, B_t = \sigma B_{xx} + \mu (A^2)_{xx}, x\in R, t>0, where \mu > \sigma >0. It plays an important role as a Ginzburg-Landau equation with a mean field in several fields of the applied sciences. We study the existence and stability of periodic patterns with an arbitrary minimal period L. 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 characterization of existence and stability for all solutions with A>0, spatial average <B>=0 and an arbitrary minimal period.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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