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Trend to Equilibrium for the Coagulation–Fragmentation Equation
Author(s) -
Dubovskiǐ P. B.,
Stewart I. W.
Publication year - 1996
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(19960710)19:10<761::aid-mma793>3.0.co;2-u
Subject(s) - uniqueness , mathematics , kernel (algebra) , conservation of mass , rate of convergence , convergence (economics) , constant (computer programming) , mathematical analysis , pure mathematics , thermodynamics , physics , economics , channel (broadcasting) , economic growth , computer science , electrical engineering , programming language , engineering
For a linear coagulation kernel and a constant fragmentation kernel we prove the existence of equilibrium solutions and examine asymptotic properties for time‐dependent solutions which are proved to converge to the equilibria. The rate of the convergence is estimated. It is shown also that all time‐dependent solutions with the same density can tend to only one particular steady‐state solution. In this sense the equilibrium solution is proved to be unique. Existence, uniqueness and mass conservation of time‐dependent solutions has been proved in a previous paper by the authors [10].