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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/521

Title: Existence and stability of singular patterns In a Ginzburg-Landau equation coupled with a mean field
Authors: Winter, M
Norbury, J
Wei, J
Keywords: Pattern formation
Steady-states
Conservation law
Publication Date: 2002
Publisher: IOP
Citation: Nonlinearity 15: 2077-2096
Abstract: We study singular patterns in a particular system of parabolic partial differential equations which consist of a Ginzburg-Landau equation and a mean field equation. We prove existence of the three simplest concentrated periodic stationary patterns (single spikes, double spikes, double transition layers) by composing them of more elementary patterns and solving the corresponding consistency conditions. In the case of spike patterns we prove stability for sufficiently large spatial periods by first showing that the eigenvalues do not tend to zero as the period goes to infinity and then passing in the limit to a nonlocal eigenvalue problem which can be studied explicitly. For the two other patterns we show instability by using the variational characterization of eigenvalues.
URI: http://bura.brunel.ac.uk/handle/2438/521
DOI: http://dx.doi.org/10.1088/0951-7715/15/6/315
Appears in Collections:Mathematics
School of Information Systems, Computing and Mathematics Research Papers

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