Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory

Detalhes bibliográficos
Autor(a) principal: Costa, Fernando Pestana da
Data de Publicação: 2008
Outros Autores: Sasportes, Rafael
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/1465
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.
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spelling Dynamics of a Non-Autonomous ODE System Occurring in Coagulation TheoryDynamics of non-autonomous ODEsCoagulation equationsSelf-similar behaviourAsymptotic evaluation of integralsWe 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.SpringerRepositório AbertoCosta, Fernando Pestana daSasportes, Rafael2010-05-14T10:02:55Z2008-032008-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/1465engCosta, 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. 55-851040-7294 (Print)info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:14:05Zoai:repositorioaberto.uab.pt:10400.2/1465Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:43:18.085511Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
title Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
spellingShingle Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
Costa, Fernando Pestana da
Dynamics of non-autonomous ODEs
Coagulation equations
Self-similar behaviour
Asymptotic evaluation of integrals
title_short Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
title_full Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
title_fullStr Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
title_full_unstemmed Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
title_sort Dynamics of a Non-Autonomous ODE System Occurring in Coagulation Theory
author Costa, Fernando Pestana da
author_facet Costa, Fernando Pestana da
Sasportes, Rafael
author_role author
author2 Sasportes, Rafael
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Costa, Fernando Pestana da
Sasportes, Rafael
dc.subject.por.fl_str_mv Dynamics of non-autonomous ODEs
Coagulation equations
Self-similar behaviour
Asymptotic evaluation of integrals
topic Dynamics of non-autonomous ODEs
Coagulation equations
Self-similar behaviour
Asymptotic evaluation of integrals
description 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.
publishDate 2008
dc.date.none.fl_str_mv 2008-03
2008-03-01T00:00:00Z
2010-05-14T10:02:55Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.2/1465
url http://hdl.handle.net/10400.2/1465
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 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
1040-7294 (Print)
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dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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