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Fragmentation arising from a distributional initial condition
Author(s) -
Lamb W.,
McBride A. C.,
McGuinness G. C.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1276
Subject(s) - mathematics , cauchy distribution , fragmentation (computing) , initial value problem , pure mathematics , kernel (algebra) , equicontinuity , regular polygon , mathematical analysis , mathematical economics , geometry , computer science , operating system
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.