Smith, Ann Louise and Lamb, Wilson and Langer, Matthias and McBride, Adam (2012) *Discrete fragmentation with mass loss.* Journal of Evolution Equations, 12 (1). pp. 181-201. ISSN 1424-3199

## Abstract

We examine an infinite system of ordinary differential equations that models a discrete fragmentation process in which mass loss can occur. The problem is treated as an abstract Cauchy problem, posed in an appropriate Banach space. Perturbation techniques from the theory of semigroups of operators are used to establish the existence and uniqueness of physically meaningful solutions under minimal restrictions on the fragmentation rates. In one particular case an explicit formula for the associated semigroup is obtained and this enables additional properties, such as compactness of the resolvent and analyticity of the semigroup, to be deduced. Another explicit solution of this particular fragmentation problem, in which mass is apparently created from a zero-mass initial state, is also investigated, and the theory of Sobolev towers is used to prove that the solution actually emanates from an initial infinite cluster of unit mass.

Item type: | Article |
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ID code: | 35846 |

Notes: | Added pdf document and references |

Keywords: | semigroup, discrete fragmentation, Sobolev tower, Mathematics, Mathematics (miscellaneous) |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 18 Nov 2011 05:23 |

Last modified: | 27 Mar 2014 09:50 |

URI: | http://strathprints.strath.ac.uk/id/eprint/35846 |

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