Fragmentation arising from a distributional initial condition

W. Lamb, A.C. McBride, G.C. McGuinness

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Abstract

A standard model for pure fragmentation is subjected to an initial condition of Dirac-delta type. Results for a corresponding abstract Cauchy problem are derived via the theory of equicontinuous semigroups of operators on locally convex spaces. An explicit solution is obtained for the case of a power-law kernel. Rigorous justification is thereby provided for results obtained more formally by Ziff and McGrady. Copyright © 2010 John Wiley & Sons, Ltd.
Original languageEnglish
Pages (from-to)1183-1191
Number of pages8
JournalMathematical Methods in the Applied Sciences
Volume33
Issue number10
DOIs
Publication statusPublished - 15 Jul 2010

Keywords

  • fragmentation
  • abstract cauchy problem
  • equicontinuous semigroup
  • dirac delta

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