Carr, J.; da Costa, F. P. Asymptotic behavior of solutions to the coagulation-fragmentation equations. II: Weak fragmentation. (English) Zbl 0838.60089 J. Stat. Phys. 77, No. 1-2, 89-123 (1994). 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. Cited in 1 ReviewCited in 28 Documents MSC: 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 Keywords:clustering; coagulation; fragmentation; phase transition; asymptotic behavior Citations:Zbl 0760.34044; Zbl 0594.58063 PDFBibTeX XMLCite \textit{J. Carr} and \textit{F. P. da Costa}, J. Stat. Phys. 77, No. 1--2, 89--123 (1994; Zbl 0838.60089) Full Text: DOI References: [1] J. Ball and J. Carr, Asymptotic behaviour of solutions to the Becker-Döring equation for arbitrary initial data,Proc. R. Soc. Edinburgh 108A:109–116 (1988). · Zbl 0656.58021 [2] J. Ball and J. Carr, The discrete coagulation-fragmentation equations: Existence, uniqueness, and density conservation,J. Stat. Phys. 61:203–234 (1990). · Zbl 1217.82050 · doi:10.1007/BF01013961 [3] J. Ball, J. Carr, and O. Penrose, The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions,Commun. Math. Phys. 104:657–692 (1986). · Zbl 0594.58063 · doi:10.1007/BF01211070 [4] J. Carr, Asymptotic behaviour of solutions to the coagulation-fragmentation equations. I. The strong fragmentation case,Proc. R. Soc. Edinburgh 121A:231–244 (1992). · Zbl 0760.34044 [5] J. Carr and F. P. Costa, Instantaneous gelation in coagulation dynamics,Z. Angew. Math. Phys. 43:974–983 (1992). · Zbl 0761.76011 · doi:10.1007/BF00916423 [6] M. Slemrod, Trend to equilibrium in the Becker-Döring cluster equations,Nonlinearity 2:429–443 (1989). · Zbl 0709.60528 · doi:10.1088/0951-7715/2/3/004 [7] M. Shirvani and H. van Roessel, The mass-conserving solutions of Smoluchowski’s coagulation equation: The general bilinear kernel,Z Angew. Math. Phys. 43:526–535 (1992). · Zbl 0825.76875 · doi:10.1007/BF00946244 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.