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Existence and uniqueness results for the continuous coagulation and fragmentation equation
Author(s) -
Lamb Wilson
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.496
Subject(s) - uniqueness , semigroup , mathematics , fragmentation (computing) , bounded function , mathematical analysis , computer science , operating system
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). Copyright © 2004 John Wiley & Sons, Ltd.