A distributional approach to fragmentation equations

Wilson Lamb, Adam Mcbride

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Abstract

We consider a linear integro-di®erential equation that models multiple fragmentation with inherent mass-loss. A systematic procedure is presented for constructing a space of generalised functions Z0 in which initial-value problems involving singular initial conditions such as the Dirac delta distribution can be analysed. The procedure makes use of results on sun dual semigroups and quasi-equicontinuous semigroups on locally convex spaces. The existence and uniqueness of a distributional solution to an abstract version of the initial-value problem are established for any given initial data u0 in Z0.
Original languageEnglish
Pages (from-to)511-520
Number of pages10
JournalCommunications in Applied Analysis
Volume15
Publication statusPublished - 2011

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Keywords

  • fragmentation equations
  • mathematics
  • linear integro-di®erential equation
  • convex spaces

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