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Self-similar behavior for multicomponent coagulation

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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.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University, Shanghai, 200444, P. R. China

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

  2. Tianmu College, Zhejiang Agriculture and Forestry University, Zhuji, Zhejiang Province, 311800, P. R. China

    Man-li Yang  (扬曼丽)

Authors
  1. Man-li Yang  (扬曼丽)
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  2. Zhi-ming Lu  (卢志明)
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  3. Yu-lu Liu  (刘宇陆)
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Corresponding author

Correspondence to Zhi-ming Lu  (卢志明).

Additional information

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)

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Yang, Ml., Lu, Zm. & Liu, Yl. Self-similar behavior for multicomponent coagulation. Appl. Math. Mech.-Engl. Ed. 35, 1353–1360 (2014). https://doi.org/10.1007/s10483-014-1872-7

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  • DOI: https://doi.org/10.1007/s10483-014-1872-7

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Chinese Library Classification

2010 Mathematics Subject Classification

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