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Strongly differentiable solutions of the discrete coagulation–fragmentation equation

McBride, A.C. and Smith, A.L. and Lamb, W. (2010) Strongly differentiable solutions of the discrete coagulation–fragmentation equation. Physica D: Nonlinear Phenomena, 239 (15). pp. 1436-1445.

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Abstract

We examine an infinite system of ordinary differential equations that models the binary coagulation and multiple fragmentation of clusters. In contrast to previous investigations, our analysis does not involve finite-dimensional truncations of the system. Instead, we treat the problem as an infinite-dimensional differential equation, posed in an appropriate Banach space, and apply perturbation results from the theory of strongly continuous semigroups of operators. The existence and uniqueness of physically meaningful solutions are established for uniformly bounded coagulation rates but with no growth restrictions imposed on the fragmentation rates.