### Abstract

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 |

### Fingerprint

### Keywords

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

### Cite this

*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

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*Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics.*1 edn, vol. 1048, AIP Conference Proceedings, pp. 942-945, International Conference on Numerical Analysis and Applied Mathematics 2008, Kos, Greece, 16/09/08. https://doi.org/10.1063/1.2991091

**Stability for a class of equilibrium solutions to the coagulation-fragmentation equation.** / Lamb, Wilson; Stewart, Iain W.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Stability for a class of equilibrium solutions to the coagulation-fragmentation equation

AU - Lamb, Wilson

AU - Stewart, Iain W.

PY - 2008/9/20

Y1 - 2008/9/20

N2 - 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.

AB - 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.

KW - coagulation–fragmentation

KW - stability of equilibria

KW - numerical analysis

KW - applied mathematics

U2 - 10.1063/1.2991091

DO - 10.1063/1.2991091

M3 - Chapter

SN - 9780735405769

VL - 1048

T3 - AIP Conference Proceedings

SP - 942

EP - 945

BT - Numerical Analysis and Applied Mathematics

ER -