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Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
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Orientador(es)
Resumo(s)
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.
Descrição
Palavras-chave
Dynamics of non-autonomous ODEs Coagulation equations Self-similar behaviour Asymptotic evaluation of integrals
Contexto Educativo
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
Editora
Springer