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Asymptotic behavior of solutions to the coagulation-fragmentation equations. II: Weak fragmentation. (English) Zbl 0838.60089
Summary: [For part I (by the first author) see Proc. R. Soc. Edinb., Sect. A 121, No. 3-4, 231–244 (1992; Zbl 0760.34044).]
The discrete coagulation-fragmentation equations are a model for the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones. The assumptions made on the fragmentation coefficients have the physical interpretation that surface effects are important. Our results on the asymptotic behavior of solutions generalize the corresponding results of J. M. Ball, the first author, and O. Penrose [Commun. Math. Phys. 104, 657–692 (1986; Zbl 0594.58063)] for the Becker-Döring equation.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
34D05 Asymptotic properties of solutions to ordinary differential equations
82B26 Phase transitions (general) in equilibrium statistical mechanics
82D60 Statistical mechanics of polymers
Full Text: DOI
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