The discrete fragmentation equations: semigroups, compactness and asynchronous exponential growth

Jacek Banasiak, Wilson Lamb

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Abstract

In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible.
Original languageEnglish
Pages (from-to)223-236
Number of pages14
JournalKinetic and Related Models
Volume5
Issue number2
DOIs
Publication statusPublished - Jun 2012

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Keywords

  • semigroups of operators
  • fragmentation
  • long time asymptotics
  • compactness
  • asynchronous exponential growth property

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