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A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels
Author(s) -
Stewart I. W.,
Meister E.
Publication year - 1989
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.1670110505
Subject(s) - mathematics , compact space , kernel (algebra) , existence theorem , fragmentation (computing) , mathematical analysis , pure mathematics , space (punctuation) , linguistics , philosophy , computer science , operating system
In this article an existence theorem is proved for the coagulation–fragmentation equation with unbounded kernel rates. Solutions are shown to be in the space X + = { c ∈ L 1 : ∫ 0 ∞(1 + x )∣ c ( x )∣d x < ∞} whenever the kernels satisfy certain growth properties and the non‐negative initial data belong to X + . The proof is based on weak L 1 compactness methods applied to suitably chosen approximating equations.