Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition
Autor(a) principal: | |
---|---|
Data de Publicação: | 2016 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/5096 |
Resumo: | We establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modeling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the similarity profile. The proof relies on a change of variables that allows for the decoupling of the original infinite system of ordinary differential equations into a closed two-dimensional nonlinear system for the monomer--bulk dynamics and a lower triangular infinite dimensional linear one for the cluster dynamics. The detailed knowledge of the long time monomer concentration, which was obtained earlier by Costin et al. in [Commun. Inf. Syst., 13 (2013), pp. 183--200] using asymptotic methods and is rederived here by center manifold arguments, is then used for the asymptotic evaluation of an integral representation formula for the concentration of j-clusters. The use of higher order expressions, both for the Stirling expansion and for the monomer evolution at large times, allow us to obtain not only the similarity limit, but also the rate at which it is approached. |
id |
RCAP_d9bbbfcb913051ef4add0d8d9ddf1e47 |
---|---|
oai_identifier_str |
oai:repositorioaberto.uab.pt:10400.2/5096 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial conditionDynamics of ODEsCoagulation processesConvergence to scaling behaviorAsymptotic evaluation of integralsSubmonolayer deposition modelWe establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modeling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the similarity profile. The proof relies on a change of variables that allows for the decoupling of the original infinite system of ordinary differential equations into a closed two-dimensional nonlinear system for the monomer--bulk dynamics and a lower triangular infinite dimensional linear one for the cluster dynamics. The detailed knowledge of the long time monomer concentration, which was obtained earlier by Costin et al. in [Commun. Inf. Syst., 13 (2013), pp. 183--200] using asymptotic methods and is rederived here by center manifold arguments, is then used for the asymptotic evaluation of an integral representation formula for the concentration of j-clusters. The use of higher order expressions, both for the Stirling expansion and for the monomer evolution at large times, allow us to obtain not only the similarity limit, but also the rate at which it is approached.The work of these authors was partially funded by FCT/Portugal through project RD0447/CAMGSD/2015. Departamento de Matemática, and Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, Universidade de Lisboa, Lisboa 1049-001, Portugal. The work of this author was partially funded by FCT/Portugal through project RD0447/CAMGSD/2015.Society for Industrial and Applied MathematicsRepositório AbertoCosta, Fernando Pestana daPinto, João TeixeiraSasportes, Rafael2016-03-31T14:46:05Z2016-03-042016-03-04T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/5096engCosta, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael - Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the Iiitial condition. "SIAM Journal of Mathematical Analysis" [Em linha]. ISSN 0036-1410 (Print) 1095-7154 (Online). Vol. 48, nº 2 (2016), p. 1109–11270036-141010.1137/15M1035033info: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:RCAAP2023-11-16T15:21:33Zoai:repositorioaberto.uab.pt:10400.2/5096Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:45:56.334893Repositório 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 |
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition |
title |
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition |
spellingShingle |
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition Costa, Fernando Pestana da Dynamics of ODEs Coagulation processes Convergence to scaling behavior Asymptotic evaluation of integrals Submonolayer deposition model |
title_short |
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition |
title_full |
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition |
title_fullStr |
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition |
title_full_unstemmed |
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition |
title_sort |
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition |
author |
Costa, Fernando Pestana da |
author_facet |
Costa, Fernando Pestana da Pinto, João Teixeira Sasportes, Rafael |
author_role |
author |
author2 |
Pinto, João Teixeira Sasportes, Rafael |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Costa, Fernando Pestana da Pinto, João Teixeira Sasportes, Rafael |
dc.subject.por.fl_str_mv |
Dynamics of ODEs Coagulation processes Convergence to scaling behavior Asymptotic evaluation of integrals Submonolayer deposition model |
topic |
Dynamics of ODEs Coagulation processes Convergence to scaling behavior Asymptotic evaluation of integrals Submonolayer deposition model |
description |
We establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modeling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the similarity profile. The proof relies on a change of variables that allows for the decoupling of the original infinite system of ordinary differential equations into a closed two-dimensional nonlinear system for the monomer--bulk dynamics and a lower triangular infinite dimensional linear one for the cluster dynamics. The detailed knowledge of the long time monomer concentration, which was obtained earlier by Costin et al. in [Commun. Inf. Syst., 13 (2013), pp. 183--200] using asymptotic methods and is rederived here by center manifold arguments, is then used for the asymptotic evaluation of an integral representation formula for the concentration of j-clusters. The use of higher order expressions, both for the Stirling expansion and for the monomer evolution at large times, allow us to obtain not only the similarity limit, but also the rate at which it is approached. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-03-31T14:46:05Z 2016-03-04 2016-03-04T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.2/5096 |
url |
http://hdl.handle.net/10400.2/5096 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael - Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the Iiitial condition. "SIAM Journal of Mathematical Analysis" [Em linha]. ISSN 0036-1410 (Print) 1095-7154 (Online). Vol. 48, nº 2 (2016), p. 1109–1127 0036-1410 10.1137/15M1035033 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics |
publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799135032726519808 |