Fragmentation arising from a distributional initial condition

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
LanguageEnglish
Pages1183-1191
Number of pages8
JournalMathematical Methods in the Applied Sciences
Volume33
Issue number10
DOIs
Publication statusPublished - 15 Jul 2010

Fingerprint

Fragmentation
Initial conditions
Abstract Cauchy Problem
Semigroups of Operators
Locally Convex Space
Explicit Solution
Justification
Paul Adrien Maurice Dirac
Standard Model
Power Law
kernel

Keywords

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

Cite this

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Fragmentation arising from a distributional initial condition. / Lamb, W.; McBride, A.C.; McGuinness, G.C.

In: Mathematical Methods in the Applied Sciences, Vol. 33, No. 10, 15.07.2010, p. 1183-1191.

Research output: Contribution to journalArticle

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