On a class of continuous fragmentation equations with singular initial conditions

C.G. McGuiness, Wilson Lamb, Adam Mcbride

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider a class of fragmentation equations in which the distribution of daughter particles formed when a parent particle fragments is governed by a homogeneous function. A systematic procedure is presented for constructing a space of distributions in which initial-value problems involving singular initial conditions can be analysed. This procedure makes use of results on sun dual semigroups and equicontinuous semigroups on locally convex spaces. Explicit solutions are obtained for the case when the fragmentation processes are governed by power-law kernels and have monodisperse initial conditions modelled by Dirac delta distributions
Original languageEnglish
Pages (from-to)1181-1192
Number of pages12
JournalMathematical Methods in the Applied Sciences
Volume34
Early online date15 Feb 2011
DOIs
Publication statusPublished - 2011

Keywords

  • one parameter semigroups
  • generalized functions
  • fragmentation equation

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