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Remarks on accessible steady states for some coagulation-fragmentation systems

Herrero, Miguel A. and Rodrigo, Marianito R. (2007) Remarks on accessible steady states for some coagulation-fragmentation systems. Discrete and Continuous Dynamical Systems. Series A., 17 (3). pp. 541-552. ISSN 1078-0947

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Abstract

In this paper we consider some systems of ordinary differential equations which are related to coagulation-fragmentation processes. In particular, we obtain explicit solutions {c(k)(t)} of such systems which involve certain coefficients obtained by solving a suitable algebraic recurrence relation. The coefficients are derived in two relevant cases: the high-functionality limit and the Flory-Stockmayer model. The solutions thus obtained are polydisperse (that is, c(k)(0) is different from zero for all k >= 1) and may exhibit monotonically increasing or decreasing total mass. We also solve a monodisperse case (where c(1)(0) is different from zero but c(k)(0)is equal to zero for all k >= 2) in the high-functionality limit. In contrast to the previous result, the corresponding solution is now shown to display a sol-gel transition when the total initial mass is larger than one, but not when such mass is less than or equal to one.

Item Type:Article
Uncontrolled Keywords:Coagulation-fragmentation; exact solutions; gelation; sol-gel transition; molecular-size distribution; diffusion; equations; kinetics; polymerization; aggregation; equilibrium; existence; polymers
Subjects:Sciences > Mathematics > Differential equations
Medical sciences > Medicine > Hematology
ID Code:16325
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