Bhowmik, S. K. and Duncan, D. B. and Grinfeld, M. and Lord, G. J. (2011) Finite to infinite steady state solutions, bifurcations of an integrodifferential equation. Discrete and Continuous Dynamical Systems  Series B, 16 (1). pp. 5771. ISSN 15313492

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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 , integrodiﬀerential 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 
Depositing user:  Pure Administrator 
Date Deposited:  24 Oct 2011 11:47 
Last modified:  27 Mar 2015 01:29 
URI:  http://strathprints.strath.ac.uk/id/eprint/35064 
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