Sol-gel transition in a coagulation-diffusion model
| dc.contributor.author | Herrero, Miguel A. | |
| dc.contributor.author | Velázquez, J.J. L. | |
| dc.contributor.author | Wrzosek, D. | |
| dc.date.accessioned | 2023-06-20T16:59:37Z | |
| dc.date.available | 2023-06-20T16:59:37Z | |
| dc.date.issued | 2000-07-15 | |
| dc.description.abstract | We consider an infinite system of reaction-diffusion equations which describes the dynamics of cluster growth, and show that there are solutions which exist for all times and exhibit a sol-gel transition in a finite time. The manner in which such transition occurs is discussed, and a gelation profile is derived. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16675 | |
| dc.identifier.doi | 10.1016/S0167-2789(00)00034-8 | |
| dc.identifier.issn | 0167-2789 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0167278900000348 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57587 | |
| dc.issue.number | 3-4 | |
| dc.journal.title | Physica D-Nonlinear Phenomena | |
| dc.language.iso | eng | |
| dc.page.final | 247 | |
| dc.page.initial | 221 | |
| dc.publisher | Elsevier | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.956.4 | |
| dc.subject.keyword | Sol-gel transition | |
| dc.subject.keyword | coagulation-diffusion model | |
| dc.subject.keyword | cluster growth | |
| dc.subject.keyword | semilinear parabolic equations | |
| dc.subject.keyword | fragmentation equations | |
| dc.subject.keyword | existence | |
| dc.subject.keyword | blow | |
| dc.subject.keyword | kinetics | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Sol-gel transition in a coagulation-diffusion model | |
| dc.type | journal article | |
| dc.volume.number | 141 | |
| dcterms.references | M. Smoluchowski, Drei Vorträge über Diffusion, Brownische Bewegung und Koagulation von Kolloiden, Physik Z 17 (1916) 557–585. S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Mod. Phys. 15 (1) (1943) 1–91. E.M. Hendriks, M.H. Ernst, R.M. Zoft, Coagulation equations with gelation, J. Stat. Phys. 31 (1983) 519–563. G. Szell, R.M. Ziff, Kinetics of polymer gelation, J. Chem. Phys. 73 (1980) 3492–3499. R.M. Ziff, Kinetics of polymerization, J. Stat. Phys. 23 (1980) 241–263. R.L. Drake, A general mathematical survey of the coagulation equation, in: G.M. Hildy, J.R. Brok (Eds.), Topics in Current Aerosol Research, Part. 2, Pergamon Press, Oxford, 1972, pp. 203–237. P.B. Dubovski, Mathematical Theory of Coagulation, Lecture Notes Series, Vol. 23, Seoul National University, 1994. J.B. Mc Leod, On an infinite set of non-linear differential equations, Quart. J. Math. Oxford 2 (1962) 119–128. R. Long, N.X. Xanh, Smoluchowski’s theory of coagulation in colloids holds rigorously in the Boltzmann–Grad limit, Z. Wahrsch. verw. Gebiete 54 (1980) 227–280. P.G.J. Van Dongen, Spatial fluctuations in reaction-limited aggregation, J. Stat. Phys. 54 (1989) 221–271. M. Slemrod, Coagulation diffusion systems: derivation and existence of solutions for the diffuse interface structure equations, Physica D 46 (1990) 351–361. F. Leyvraz, H.R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A 14 (1981) 3389–3405. J.M. Ball, J. Carr, The discrete coagulation–fragmentation equations: existence, uniqueness and density conservation, J. Stat. Phys. 61 (1990) 203–234. D. Wrzosek, Existence of solutions for the discrete coagulation–fragmentation model with diffusion, Topol. Meth. Nonlinear Anal. 9 (1997) 279–296. P.J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, NY, USA, 1953. F. Leyvraz, Existence and properties of post-gel solutions for the kinetic equations of coagulation, J. Phys. A 16 (1983) 2861–2873. H. Jeon, Existence of gelling solutions for coagulation fragmentation equations, Commun. Math. Phys. 194 (1998) 541–567. F.P. Costa, A finite dimensional dynamical model for gelation in coagulation processes, J. Nonlinear Sci. 8 (1998) 619–653. Ph. Bénilan, D. Wrzosek, On an infinite system of reaction–diffusion equations, Adv. Math. Sci. Appl. 7 (1997) 351–366. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1997. L.C. Evans, Weak convergence methods for nonlinear partial differential equations, Am. Math. Soc. Regional Conference Series in Mathematics, Vol. 74, American Mathematical Society, Providence, RI, 1990. M.A. Herrero, E. Medina, J.J.L. Velázquez, The birth of a cusp in the two-dimensional, undercooled Stefan problem, Quart. J. App. Math., in press. M.A. Herrero, J.J.L. Velázquez, Blow-up behaviour of one-dimensional semilinear parabolic equations, Ann. Inst. Henri Poincaré 10 (2) (1993) 131–189. M.A. Herrero, J.J.L. Velázquez, Blow-up profiles in one-dimensional semilinear parabolic problems, Commun. PDE 17 (1992) 205–219. J.J.L. Velázquez, Higher-dimensional blow-up for semilinear parabolic equations, Commun. PDE 17 (1992) 1567–1596. Ph. Laurençot, Global solutions to the discrete coagulation equations, submitted for publication. V. Komornik, Exact Controllability and Stabilization, Masson, Paris, 1994. P. Baras, J.C. Hassan, L. Veron, Compacité de l’operateur definissant la solution d’une equation d’evolution non homogène, C.R. Acad. Sci. Paris Ser. I 284 (1977) 799–802. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983 | |
| dspace.entity.type | Publication |
Download
Original bundle
1 - 1 of 1