Yang M.-L.,Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University |
Yang M.-L.,Zhejiang Agriculture And forestry University |
Lu Z.-M.,Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University |
Liu Y.-L.,Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University
Applied Mathematics and Mechanics (English Edition) | Year: 2014
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. © 2014, Shanghai University and Springer-Verlag Berlin Heidelberg.