### Abstract

Smoluchowski's coagulation equation for irreversible aggregation with constant kernel is considered in its discrete version[Figure not available: see fulltext.] where c_{t}=c_{1}(t) is the concentration of l-particle clusters at time t. We prove that for initial data satisfying c_{1}(0)>0 and the condition 0 =c_{l}(0) <A (1+?)^{-l}(A ?>0), the solutions behave asymptotically like c_{1}(t)~t^{-2}˜c(lt^{-1}) as t?8 with lt^{-1} kept fixed. The scaling function ˜c(?) is (1/gr)?, where {Mathematical expression}, a conserved quantity, is the initial number of particles per unit volume. An analous result is obtained for the continuous version of Smoluchowski's coagulation equation {Mathematical expression} where c(v, t) is the oncentration of clusters of size v. © 1994 Plenum Publishing Corporation.

Original language | English |
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Pages (from-to) | 389-407 |

Number of pages | 19 |

Journal | Journal of Statistical Physics |

Volume | 75 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - May 1994 |

### Keywords

- cluster growth
- dynamical scaling
- kinetics of first-order phase transitions
- Smoluchowski's coagulation equations