## 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.

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.

Original language | English |
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Pages (from-to) | 57-71 |

Number of pages | 15 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 16 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 2011 |

## Keywords

- bifurcations
- integro-diﬀerential equations
- steady state solutions