Strongly differentiable solutions of the discrete coagulation–fragmentation equation

A.C. McBride, A.L. Smith, W. Lamb

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1436-1445
Number of pages10
JournalPhysica D: Nonlinear Phenomena
Issue number15
Publication statusPublished - 1 Aug 2010


  • semigroups of operators
  • fragmentation
  • coagulation
  • semilinear Cauchy problems


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