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The formation of a distribution of cluster sizes is a common feature in a wide variety of situations. Examples include astrophysics, atmospheric physics and polymer science, [2, 3, 8]. In this paper we discuss some mathematical aspects of the Smoluchowski coagulation equation which is a model for the dynamics of cluster growth. This model involves a coupled… (More)

For a coagulation equation with Becker-Döring type interactions and time-independent monomer input we study the detailed long-time behaviour of nonnegative solutions and prove the convergence to a selfsimilar function.

In this paper we generalize recent results of Kreer and Penrose by showing that solutions to the discrete Smoluchowski equations ċj = j−1 ∑ k=1 cj−kck − 2cj ∞ ∑ k=1 ck, j = 1, 2, . . . with general exponentially decreasing initial data, with density ρ, have the following asymptotic behaviour lim j, t→∞ ξ=j/t fixed j∈J tcj(t) = q ρ e−ξ/ρ, where J = {j :… (More)

We consider a cluster system in which each cluster is characterized by two parameters: an “order” i, following Horton-Strahler’s rules, and a “mass” j following the usual additive rule. Denoting by ci,j(t) the concentration of clusters of order i and mass j at time t, we derive a coagulationlike ordinary differential system for the time dynamics of these… (More)

Abstract. We consider a coagulation model first introduced by Redner, Ben-Avraham and Kahng in [11], the main feature of which is that the reaction between a j-cluster and a k-cluster results in the creation of a |j − k|-cluster, and not, as in Smoluchowski’s model, of a (j + k)-cluster. In this paper we prove existence and uniqueness of solutions under… (More)

- Fernando P. da Costa, Joao T. Pinto, Rafael Sasportes
- SIAM J. Math. Analysis
- 2016

We establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modelling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the… (More)

In this work we study the rate of convergence to similarity profiles in a mean field model for the deposition of a submonolayer of atoms in a crystal facet, when there is a critical minimal size n ≥ 2 for the stability of the formed clusters. The work complements recently published related results by the same authors in which the rate of convergence was… (More)

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