On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations

Costa, Fernando Pestana da

http://hdl.handle.net/10400.2/1470

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Authors

Costa, Fernando Pestana da

Abstract(s)

In this paper we generalize recent results of Kreer and Penrose by showing that solutions to the discrete Smoluchowski equations $$\dot{c}_{j} = \sum_{k=1}^{j-1}c_{j-k}c_{k} - 2c_{j}\sum_{k=1}^{\infty}c_{k}, j = 1, 2, \ldots$$ with general exponentially decreasing initial data, with density $\rho,$ have the following asymptotic behaviour $$\lim_{j, t \rightarrow\infty, \xi = j/t fixed, j \in {\cal J}} t^{2}c_{j}(t) = \frac{q}{\rho}\, e^{-\xi/\rho},$$ where ${\cal J} = \{j: c_{j}(t)>0, t>0\}$ and $q =\gcd \{j: c_{j}(0)>0\}.$

Keywords

Smoluchowski coagulation equations Self-similar solutions

URI

http://hdl.handle.net/10400.2/1470

Citation

Costa, Fernando Pestana da - On the dynamic scaling behaviour of solutions to the discrete Smoluchowski equations. "Proceedings of the Edinburgh Mathematical Society" [Em linha]. ISSN 0013-0915 (Print)1464-3839 (Online). Nº 39 (1996), p. 547-559