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On a non‐uniqueness in fragmentation models
Author(s) -
Banasiak J.
Publication year - 2002
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.301
Subject(s) - uniqueness , mathematics , fragmentation (computing) , simplicity , class (philosophy) , mathematical economics , calculus (dental) , pure mathematics , mathematical analysis , computer science , physics , artificial intelligence , quantum mechanics , operating system , medicine , dentistry
Abstract Equations of fragmentation describing e.g. the polymer degradation, despite their apparent simplicity, have numerous non‐typical features. One of them is the existence of multiple solutions. In this paper, applying classical results of Hille and Phillips, we explain their occurrence and prove that nevertheless the uniqueness holds for a large class of physically reasonable solutions. Copyright © 2002 John Wiley & Sons, Ltd.