Publication
Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition
| dc.contributor.author | Costa, Fernando Pestana da | |
| dc.contributor.author | Pinto, João Teixeira | |
| dc.contributor.author | Sasportes, Rafael | |
| dc.date.accessioned | 2016-03-31T14:46:05Z | |
| dc.date.available | 2016-03-31T14:46:05Z | |
| dc.date.issued | 2016-03-04 | |
| dc.description.abstract | 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. | pt_PT |
| dc.description.sponsorship | 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. | |
| dc.identifier.citation | 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 | pt_PT |
| dc.identifier.doi | 10.1137/15M1035033 | pt_PT |
| dc.identifier.issn | 0036-1410 | |
| dc.identifier.issn | 1095-7154 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/5096 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Society for Industrial and Applied Mathematics | pt_PT |
| dc.relation.publisherversion | http://epubs.siam.org/doi/abs/10.1137/15M1035033 | pt_PT |
| dc.subject | Dynamics of ODEs | pt_PT |
| dc.subject | Coagulation processes | pt_PT |
| dc.subject | Convergence to scaling behavior | pt_PT |
| dc.subject | Asymptotic evaluation of integrals | pt_PT |
| dc.subject | Submonolayer deposition model | pt_PT |
| dc.title | Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.conferencePlace | Philadelphia, PA | pt_PT |
| oaire.citation.endPage | 1127 | pt_PT |
| oaire.citation.startPage | 1109 | pt_PT |
| oaire.citation.title | SIAM Journal of Mathematical Analysis | pt_PT |
| oaire.citation.volume | 48 | pt_PT |
| person.familyName | Costa | |
| person.familyName | Teixeira Pinto | |
| person.familyName | Sasportes | |
| person.givenName | Fernando Pestana da | |
| person.givenName | João | |
| person.givenName | Rafael | |
| person.identifier.ciencia-id | 1610-6502-E6C5 | |
| person.identifier.ciencia-id | DC16-AE64-30AE | |
| person.identifier.orcid | 0000-0002-9072-797X | |
| person.identifier.orcid | 0000-0003-0190-2113 | |
| person.identifier.orcid | 0000-0003-2855-9490 | |
| person.identifier.rid | K-5942-2013 | |
| person.identifier.scopus-author-id | 14827970300 | |
| person.identifier.scopus-author-id | 7402584922 | |
| person.identifier.scopus-author-id | 24176381600 | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
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| relation.isAuthorOfPublication.latestForDiscovery | 72748d24-0598-4f36-804e-87eebd0d06af |