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Symmetries and exact solutions of the population balance equation with growth and breakage processes, using group analysis
Author(s) -
Lin Fubiao,
Zhang Qianhong
Publication year - 2020
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.6997
Subject(s) - mathematics , homogeneous space , population balance equation , breakage , invariant (physics) , population , mathematical analysis , balance (ability) , mathematical physics , geometry , computer science , sociology , world wide web , physical medicine and rehabilitation , medicine , demography
Population balance equation which may be employed to handle a wide variety of particle processes has certainly received unprecedented attention, but the absence of explicit exact solutions necessitates the use of numerical approaches. The one‐dimensional population balance equation with time independent but size dependent growth and breakage rate is investigated. The corresponding system of equation is solved analytically by use of the Lie group analysis method. Symmetries, reduced equations, invariant solutions, explicit exact, and unphysical solutions are presented in this paper.