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Remarks on accessible steady states for some coagulation-fragmentation systems

Journal Article


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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 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, is different from zero for all ) and may exhibit monotonically increasing or decreasing total mass. We also solve a monodisperse case (where is different from zero but is equal to zero for all ) 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.

Publication Date


  • 2007

Citation


  • Herrero, M. A. & Rodrigo, M. R. (2007). Remarks on accessible steady states for some coagulation-fragmentation systems. Discrete and Continuous Dynamical Systems Series A, 17 (3), 541-552.

Scopus Eid


  • 2-s2.0-34247253855

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2875&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1866

Number Of Pages


  • 11

Start Page


  • 541

End Page


  • 552

Volume


  • 17

Issue


  • 3

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 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, is different from zero for all ) and may exhibit monotonically increasing or decreasing total mass. We also solve a monodisperse case (where is different from zero but is equal to zero for all ) 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.

Publication Date


  • 2007

Citation


  • Herrero, M. A. & Rodrigo, M. R. (2007). Remarks on accessible steady states for some coagulation-fragmentation systems. Discrete and Continuous Dynamical Systems Series A, 17 (3), 541-552.

Scopus Eid


  • 2-s2.0-34247253855

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2875&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1866

Number Of Pages


  • 11

Start Page


  • 541

End Page


  • 552

Volume


  • 17

Issue


  • 3