On a coagulation and fragmentation equation with mass loss

J. Banasiak, W. Lamb

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


A nonlinear integro-differential equation that models a coagulation and multiple fragmentation process in which continuous and discrete fragmentation mass loss can occur is examined using the theory of strongly continuous semigroups of operators. Under the assumptions that the coagulation kernel is constant, the fragmentation-rate function is linearly bounded, and the continuous mass-loss-rate function is locally Lipschitz, global existence and uniqueness of solutions that lose mass in accordance with the model are established. In the case when no coagulation is present and the fragmentation process is binary with constant fragmentation kernel and constant continuous mass loss, an explicit formula is given for the associated substochastic semigroup.
Original languageEnglish
Pages (from-to)1157-1173
Number of pages16
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Issue number6
Publication statusPublished - Dec 2006


  • coagulation
  • fragmentation
  • equation
  • mass


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