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Existence and uniqueness results for the continuous coagulation and fragmentation equation

Lamb, W. (2004) Existence and uniqueness results for the continuous coagulation and fragmentation equation. Mathematical Methods in the Applied Sciences, 27 (6). pp. 703-721. ISSN 0170-4214

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Abstract

A non-linear integro-differential equation modelling coagulation and fragmentation is investigated using the theory of strongly continuous semigroups of operators. Under the assumptions that the coagulation kernel is bounded and the overall rate of fragmentation satisfies a linear growth condition, global existence and uniqueness of mass-conserving solutions are established. This extends similar results obtained in earlier investigations. In the case of pure fragmentation, when no coagulation occurs, a precise characterization of the generator of the associated semigroup is also obtained by using perturbation results for substochastic semigroups due to Banasiak (Taiwanese J. Math. 2001; 5: 169-191) and Voigt (Transport Theory Statist. Phys. 1987; 16: 453-466).

Item type: Article
ID code: 2182
Keywords: semigroups of operators, semilinear Cauchy problem, coagulation, fragmentation, Mathematics, Engineering(all), Mathematics(all)
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Strathprints Administrator
    Date Deposited: 05 Jan 2007
    Last modified: 04 Sep 2014 12:36
    URI: http://strathprints.strath.ac.uk/id/eprint/2182

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