Dynamics of a non-autonomous ODE system occurring in coagulation theory

Journal of Dynamics and Differential Equations

Volumn 20, Issue 1, 2008, Pages 55-85

  Da Costa, F P ^a,b   Sasportes, Rafael ^a  

^a UNIVERSIDADE ABERTA   (Portugal)

^b INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Asymptotic evaluation of integrals; Coagulation equations; Dynamics of non autonomous ODEs; Self similar behaviour

Indexed keywords

EID: 43349091883     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-006-9067-5     Document Type: Article

References (14)

1. Ablowitz M.J., Fokas A.S. (2003). Complex Variables, 2nd Edn., Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge
2. Ball J.M., Carr J., Penrose O. (1986). The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions. Comm. Math. Phys. 104, 657-692
3. Bartelt M.C., Evans J.W. (1996). Exact island-size distributions for submonolayer deposition: influence of correlations between island size and separation. Phys. Rev. B 54, R17359-R17362
4. Brilliantov N.V., Krapivsky P.L. (1991). Non-scaling and source-induced scaling behaviour in aggregation models of movable monomers and immovable clusters. J. Phys. A; Math. Gen. 24, 4787-4803
5. da Costa F.P., van Roessel H., Wattis J.A.D., (2006). Long-time behaviour and self-similarity in a coagulation equation with input of monomers. Markov Processes Relat. Fields 12, 367-398
6. Fournier N., Laurençot Ph., (2005). Existence of self-similar solutions to Smoluchowski's coagulation equation. Commun. Math. Phys. 256, 589-609
7. Hendriks E.M., Ernst M.H., (1984). Exactly soluble addition and condensation models in coagulation kinetics. J. Coll. Int. Sci. 97, 176-194
8. Laurençot Ph., Mischler S. (2004). On Coalescence equations and related models. In: Degond P., Pareschi L., Russo G. (eds), Modelling and Computational Methods for Kinetic Equations. Birkhäuser, Boston, pp. 321-356
9. Leyvraz F. (2003). Scaling theory and exactly solved models in the kinetics of irreversible aggregation. Phys. Rep. 383, 95-212
10. Leyvraz F. (2005). Rigorous results in the scaling theory of irreversible aggregation kinetics. J. Nonlinear Math. Phys. 12 (Suppl 1): 449-465
11. Menon G., Pego R.L., (2004). Approach to self-similarity in Smoluchowski's coagulation equations. Commun. Pure Appl. Math. 57: 1197-1232
12. Menon G., Pego R.L. (2005). Dynamical scaling in Smoluchowski's coagulation equations: uniform convergence. SIAM J. Math. Anal. 36, 1629-1651
13. Penrose O. (1989). Metastable states for the Becker-Döring cluster equations. Commun. Math. Phys. 124, 515-541
14. Wattis J.A.D. (2004). Similarity solutions of a Becker-Döring system with time-dependent monomer input. J. Phys. A: Math. Gen. 37: 7823-7841