Fragmentation arising from a distributional initial condition | Zendy

Lamb W. | Zendy; McBride A. C. | Zendy; McGuinness G. C. | Zendy

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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.

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