Applied Mathematics and Mechanics

, Volume 35, Issue 11, pp 1353–1360 | Cite as

Self-similar behavior for multicomponent coagulation

  • Man-li Yang (扬曼丽)
  • Zhi-ming Lu (卢志明)
  • Yu-lu Liu (刘宇陆)


Self-similar behavior for the multicomponent coagulation system is investigated analytically in this paper. Asymptotic self-similar solutions for the constant kernel, sum kernel, and product kernel are achieved by introduction of different generating functions. In these solutions, two size-scale variables are introduced to characterize the asymptotic distribution of total mass and individual masses. The result of product kernel (gelling kernel) is consistent with the Vigli-Ziff conjecture to some extent. Furthermore, the steady-state solution with injection for the constant kernel is obtained, which is again the product of a normal distribution and the scaling solution for the single variable coagulation.

Key words

multicomponent coagulation self-similar solution generating function 

Chinese Library Classification


2010 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Man-li Yang (扬曼丽)
    • 1
    • 2
  • Zhi-ming Lu (卢志明)
    • 1
  • Yu-lu Liu (刘宇陆)
    • 1
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai Key Laboratory of Mechanics in Energy Engineering Shanghai UniversityShanghaiP. R. China
  2. 2.Tianmu CollegeZhejiang Agriculture and Forestry UniversityZhuji, Zhejiang ProvinceP. R. China

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