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Existence and uniqueness results for the non‐autonomous coagulation and multiple‐fragmentation equation
Author(s) -
McLaughlin D. J.,
Lamb W.,
McBride A. C.
Publication year - 1998
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/(sici)1099-1476(19980725)21:11<1067::aid-mma985>3.0.co;2-x
Subject(s) - uniqueness , fragmentation (computing) , mathematics , initial value problem , operator (biology) , contraction mapping , mathematical analysis , computer science , chemistry , fixed point theorem , biochemistry , repressor , transcription factor , gene , operating system
An initial‐value problem modelling coagulation and fragmentation processes is studied. The results of earlier papers are extended to models where either one or both of the rates of coagulation and fragmentation depend on time. An abstract integral equation, involving the solution operator to the linear fragmentation part, is investigated via the contraction mapping principle. A unique global, non‐negative, mass‐conserving solution to this abstract equation is shown to exist. The latter solution is used to generate a global, non‐negative, mass‐conserving solution to the original non‐autonomous coagulation and multiple‐fragmentation equation. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.