Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.2/1465
Título: Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
Autor: Costa, Fernando Pestana da
Sasportes, Rafael
Palavras-chave: Dynamics of non-autonomous ODEs
Coagulation equations
Self-similar behaviour
Asymptotic evaluation of integrals
Data: Mar-2008
Editora: Springer
Citação: Costa, Fernando; Sasportes, Rafael - Dynamics of a non-autonomous ODE System occurring in Coagulation Theory. "Journal of Dynamics and Differential Equations" [Em linha]. ISSN 1040-7294 (Print) 1572-9222 (Online). Vol. 20, nº 1 (March 2008), p. 55-85
Resumo: We consider a constant coefficient coagulation equation with Becker–D¨oring type interactions and power law input of monomers J1(t)=αtω, with α > 0 and ω>−1 2 . For this infinite dimensional system we prove solutions converge to similarity profiles as t and j converge to infinity in a similarity way, namely with either j/ς or (j −ς)/√ς constants, where ς =ς(t) is a function of t only. This work generalizes to the non-autonomous case a recent result of da Costa et al. (2004). Markov Processes Relat. Fields 12, 367–398. and provides a rigorous derivation of formal results obtained by Wattis J. Phys. A: Math. Gen. 37, 7823–7841. The main part of the approach is the analysis of a bidimensional non-autonomous system obtained through an appropriate change of variables; this is achieved by the use of differential inequalities and qualitative theory methods. The results about rate of convergence of solutions of the bidimensional system thus obtained are fed into an integral formula representation for the solutions of the infinite dimensional system which is then estimated by an adaptation of methods used by da Costa et al. (2004). Markov Processes Relat. Fields 12, 367–398.
URI: http://hdl.handle.net/10400.2/1465
ISSN: 1040-7294 (Print)
1572-9222 (Online)
Versão do Editor: DOI: 10.1007/s10884-006-9067-5
Aparece nas colecções:Matemática e Estatística - Artigos em revistas internacionais / Papers in international journals

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