### Abstract

We consider the behaviour of solutions to the continuous constant-rate coagulation-fragmentation equation in the vicinity of an equilibrium solution. Semigroup methods are used to show that the governing linear equation for a perturbation epsilon(x,t) has a unique globally defined solution for suitable initial conditions. In addition, Laplace transforms and the method of characteristics lead to an explicit formula for epsilon. The long-term behavior of epsilon is also discussed.

Original language | English |
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Title of host publication | Numerical Analysis and Applied Mathematics |

Subtitle of host publication | International Conference on Numerical Analysis and Applied Mathematics |

Pages | 942-945 |

Number of pages | 4 |

Volume | 1048 |

Edition | 1 |

DOIs | |

Publication status | Published - 20 Sep 2008 |

Event | International Conference on Numerical Analysis and Applied Mathematics 2008 - Kos, Greece Duration: 16 Sep 2008 → 20 Sep 2008 |

### Publication series

Name | AIP Conference Proceedings |
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Publisher | American Institute of Physics |

### Conference

Conference | International Conference on Numerical Analysis and Applied Mathematics 2008 |
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Country | Greece |

City | Kos |

Period | 16/09/08 → 20/09/08 |

### Keywords

- coagulation–fragmentation
- stability of equilibria
- numerical analysis
- applied mathematics

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## Cite this

Lamb, W., & Stewart, I. W. (2008). Stability for a class of equilibrium solutions to the coagulation-fragmentation equation. In

*Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics*(1 ed., Vol. 1048, pp. 942-945). (AIP Conference Proceedings). https://doi.org/10.1063/1.2991091