Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-07T10:30:08.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic behaviour of solutions to the Becker-Döring equations

Published online by Cambridge University Press:  20 January 2009

J. Carr  and
R. M. Dunwell
J. Carr
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton Edinburgh EH14 4AS, Scotland
R. M. Dunwell
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton Edinburgh EH14 4AS, Scotland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The asymptotics behaviour of solutions of the Becker-Döring cluster equations is determined for cases in which coagulation dominates fragmentation. We show that all non-zero solutions tend weak* to zero.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 415 - 424
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Ball, J. M. and Carr, J., Asymptotic behaviour of solutions to the Becker-Döring equations for arbitrary initial data, Proc. Roy. Soc. Edinburgh A 108 (1988), 109–116.Google Scholar
2.Ball, J. M. and Carr, J., The discrete coagulation-fragmentation equations: existence, uniqueness and density conservation, J. Stat. Phys. 61 (1990), 203–234.Google Scholar
3.Ball, J. M., Carr, J. and Penrose, O., The Becker-Döring cluster equations: Basic properties and asymptotic behaviour, Comm. Math. Phys. 104 (1986), 657–692.CrossRefGoogle Scholar
4.Becker, R. and Döring, W., Kinetische behandlung der kinetische behandlung der keimbildung in übersättigten dämpfen, Ann. Physik. 24 (1935), 719–752.Google Scholar
5.Carr, J., Asymptotic behaviour of solutions to the coagulation-fragmentation equations I: The strong fragmentation case, Proc. Roy. Soc. Edinburgh 121A (1992), 231–244.CrossRefGoogle Scholar
6.Carr, J. and Da Costa, F. P., Asymptotic behaviour of solutions to the coagulation-fragmentation equations II: Weak fragmentation, J. Stat. Phys. 77 (1994), 89–123.CrossRefGoogle Scholar
7.Carr, J., Duncan, D. B. and Walshaw, C. H., Numerical approximation of a metastable system, IMA J. Numer. Anal. 15 (1995), 505–521.CrossRefGoogle Scholar
8.Collet, J. F. and Poupaud, F., Existence of solutions to coagulation-fragmentation systems with diffusion, Transp. Theory Statist. Phys. 25 (1996), 503–513.CrossRefGoogle Scholar
9.Penrose, O., Metastable states for the Becker-Döring cluster equations, Comm. Math. Phys. 124 (1989), 515–541.CrossRefGoogle Scholar
10.Slemrod, M., Trend to equilibrium in the Becker-Döring cluster equations, Nonlinearity 2 (1987), 429–443.CrossRefGoogle Scholar
11.Slemrod, M., Coagulation-diffusion systems: derivation and existence of solutions for the diffuse interface structure equations, Phys. D. 46 (1990), 351–366.CrossRefGoogle Scholar