Trend to equilibrium for the coagulation-fragmentation equation

Mathematical Methods in the Applied Sciences

Volumn 19, Issue 10, 1996, Pages 761-772

  Dubovskii, P B ^a   Stewart, I W ^b  

^a Obninsk State Technical University for Nuclear Power Engineering   (Russian Federation)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COAGULATION; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ESTIMATION; PHASE EQUILIBRIA;

ASYMPTOTIC PROPERTIES; COAGULATION FRAGMENTATION EQUATION; EQUILIBRIUM SOLUTIONS;

MATHEMATICAL TECHNIQUES;

EID: 0030191189     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1099-1476(19960710)19:10<761::aid-mma793>3.0.co;2-u     Document Type: Review

References (15)

1. Aizenman, M. and Bak, T. A., 'Convergence to equilibrium in a system of reacting polymers'. Commun. Math. Phys., 65, 203-230 (1979).
2. Ball, J. M. and Carr, J., 'Asymptotic behaviour of solutions to the Becker-Döring equations for arbitrary initial data', Proc. Royal Soc. Edin. Sect. A., 108, 109-116 (1988).
3. Ball, J. M., Carr, J. and Penrose, O., 'The Becker-Döring cluster equations: basic properties and asymptotic behaviour of solutions', Commun. Math. Phys., 104, 657-692 (1986).
4. Barrow, J. D., 'Coagulation with fragmentation', J. Phys. A: Math. Gen., 14, 729-733 (1981).
5. Bruno, O., Friedman, A. and Reitich, F., 'Asymptotic behavior for a coalescence problem', Trans. Amer. Math. Soc., 338, 133-157 (1993).
6. Carr, J., 'Asymptotic behaviour of solutions to the coagulation-fragmentation equations. I. The strong fragmentation case', Proc. Royal Soc. Edin. Sect. A., 121, 231-244 (1992).
7. Dubovskii, P. B., 'Solutions of a spatially inhomogeneous coagulation equation with particle fractionation taken into account', Differential Equations 26, 508-513 (1990) (English translation: pp. 380-384).
8. Dubovskii, P. B., 'An iterative method for solving the coagulation equation with spatially inhomogeneous velocity fields', USSR Comput. Maths. Math. Phys., 30, 1755-1757 (1990) (English translation: pp. 116-117).
9. Dubovskii, P. B., Galkin, V. A. and Stewart, I. W., 'Exact solutions for the coagulation-fragmentation equation', J. Phys. A: Math. Gen., 25, 4737-4744 (1992).
10. Dubovskii, P. B. and Stewart I. W., 'Existence, uniqueness and mass conservation for the coagulation-fragmentation equation. Math. Meth. Appl. Sci. to appear.
11. Edwards, R. E., 'Functional Analysis' Holt, Rinehart and Winston, New York, 1965.
12. Gajewski, H. 'On a first order partial differential equation with nonlocal nonlinearity', Math Nachrichten, 111, 289-300 (1983).
13. Penrose, O., 'Metastable states for the Becker-Döring cluster equations', Commun. Math. Phys., 121, 527-540 (1989).
14. Slemrod, M., 'Trend to equilibrium in the Becker-Döring duster equations', Nonlinearity, 2, 429-443 (1989).
15. Stewart, I. W. and Dubovskii, P. B. 'Approach to equilibrium for the coagulation-fragmentation equation via a Lyapunov functional', Math. Meth. Appl. Sci. 19, 171-185 (1996).