Discrete fragmentation with mass loss

Ann Louise Smith, Wilson Lamb, Matthias Langer, Adam McBride

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We examine an infinite system of ordinary differential equations that models a discrete fragmentation process in which mass loss can occur. The problem
is treated as an abstract Cauchy problem, posed in an appropriate Banach space. Perturbation techniques from the theory of semigroups of operators are used to establish the existence and uniqueness of physically meaningful solutions under minimal restrictions on the fragmentation rates. In one particular case an explicit formula for the associated semigroup is obtained and this enables additional properties, such as compactness of the resolvent and analyticity of the semigroup, to be deduced. Another explicit solution of this particular fragmentation problem, in which mass is apparently created from a zero-mass initial state, is also investigated, and the theory of Sobolev towers is used to prove that the solution actually emanates from an initial infinite cluster of unit mass.
Original languageEnglish
Pages (from-to)181-201
Number of pages21
JournalJournal of Evolution Equations
Issue number1
Early online date26 Nov 2011
Publication statusPublished - Mar 2012


  • semigroup
  • discrete fragmentation
  • Sobolev tower


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