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Self-similar behavior for multicomponent coagulation

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  • 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University, Shanghai 200444, P. R. China;
    2. Tianmu College, Zhejiang Agriculture and Forestry University, Zhuji 311800, Zhejiang Province, P. R. China

Received date: 2013-05-30

  Revised date: 2014-02-15

  Online published: 2014-11-01

Supported by

Project supported by the National Natural Science Foundation of China (Nos. 11272196 and 11222222) and the Zhejiang Association of Science and Technology of Soft Science Research Project (No. ZJKX14C-34)

Abstract

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.

Cite this article

Man-li YANG;Zhi-ming LU;Yu-lu LIU . Self-similar behavior for multicomponent coagulation[J]. Applied Mathematics and Mechanics, 2014 , 35(11) : 1353 -1360 . DOI: 10.1007/s10483-014-1872-7

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