×

zbMATH — the first resource for mathematics

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.

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
PDF BibTeX XML Cite
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
[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
[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
[6] M. Slemrod, Trend to equilibrium in the Becker-Döring cluster equations,Nonlinearity 2:429–443 (1989). · Zbl 0709.60528
[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
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.