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Finite to infinite steady state solutions, bifurcations of an integro-differential equation

Bhowmik, S. K. and Duncan, D. B. and Grinfeld, M. and Lord, G. J. (2011) Finite to infinite steady state solutions, bifurcations of an integro-differential equation. Discrete and Continuous Dynamical Systems - Series B, 16 (1). pp. 57-71. ISSN 1531-3492

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    Abstract

    We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid–solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi–discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem.

    Item type: Article
    ID code: 35064
    Keywords: bifurcations , integro-differential equations, steady state solutions, Mathematics, Discrete Mathematics and Combinatorics, Applied Mathematics
    Subjects: Science > Mathematics
    Department: Faculty of Engineering > Civil and Environmental Engineering
    Faculty of Science > Mathematics and Statistics
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    Depositing user: Pure Administrator
    Date Deposited: 24 Oct 2011 12:47
    Last modified: 11 Apr 2014 08:22
    URI: http://strathprints.strath.ac.uk/id/eprint/35064

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