JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (8): 125-134.doi: 10.6040/j.issn.1671-9352.0.2023.412

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Method of moments, scaling transformation group analysis and self-similar solutions of a class of 3+1-dimensional macroscopic population balance equation

LIN Fubiao, YANG Yang   

  1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China
  • Published:2025-07-25

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Abstract: Self-similar solutions and approaches for analytically solving a class of(3+1)-dimensional macroscopic population balance(integro-partial differential)equations with homogeneous collision kernels are studied.(3+1)-dimensional integro-partial differential equation is successfully transformed into(2+1)-dimensional partial differential moment equations by use of the method of moments. The admitted scaling transformation groups, reduced(2+1)-dimensional integro-partial differential equations, reduced(1+1)-dimensional ordinary differential equations, self-similar solutions, explicit exact solutions of(3+1)-dimensional integro-partial differential equations and(2+1)-dimensional partial differential moment equations are presented by use of the method of scaling transformation analysis. The dynamic behaviour analysis of the obtained solutions are also given.

Key words: macroscopic population balance equation, moment method, scaling transformation group, self-similar solution

CLC Number: 

  • O175.6
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