A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies

Autores
Amster, Pablo Gustavo; Kwong, Man Kan; Rogers, Colin
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In prior work, a series of two-point boundary value problems have been investigated for a steady state two-ion electro-diffusion model system in which the sum of the valencies ν+ and ν− is zero. In that case, reduction is obtained to the canonical Painlevé II equation for the scaled electric field. Here, a physically important Neumann boundary value problem in the generic case when ν++ν−≠0 is investigated. The problem is novel in that the model equation for the electric field involves yet to be determined boundary values of the solution. A reduction of the Neumann boundary value problem in terms of elliptic functions is obtained for privileged valency ratios. A topological index argument is used to establish the existence of a solution in the general case, under the assumption ν++ν−≤0.
Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Kwong, Man Kan. Hong Kong Polytechnic University; China
Fil: Rogers, Colin. University Of New South Wales. Faculty Of Science; Australia. Hong Kong Polytechnic University; China
Materia
Electro-Diffusion Models
Painlevé Ii
Unequal Valencies
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14879
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14879
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal ValenciesAmster, Pablo GustavoKwong, Man KanRogers, ColinElectro-Diffusion ModelsPainlevé IiUnequal Valencieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In prior work, a series of two-point boundary value problems have been investigated for a steady state two-ion electro-diffusion model system in which the sum of the valencies ν+ and ν− is zero. In that case, reduction is obtained to the canonical Painlevé II equation for the scaled electric field. Here, a physically important Neumann boundary value problem in the generic case when ν++ν−≠0 is investigated. The problem is novel in that the model equation for the electric field involves yet to be determined boundary values of the solution. A reduction of the Neumann boundary value problem in terms of elliptic functions is obtained for privileged valency ratios. A topological index argument is used to establish the existence of a solution in the general case, under the assumption ν++ν−≤0.Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Kwong, Man Kan. Hong Kong Polytechnic University; ChinaFil: Rogers, Colin. University Of New South Wales. Faculty Of Science; Australia. Hong Kong Polytechnic University; ChinaAmer Inst Mathematical Sciences2012-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14879Amster, Pablo Gustavo; Kwong, Man Kan; Rogers, Colin; A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems-series B; 17; 7; 10-2012; 2299-23111531-3492enginfo:eu-repo/semantics/altIdentifier/url/https://aimsciences.org/journals/displayArticlesnew.jsp?paperID=7475info:eu-repo/semantics/altIdentifier/doi/10.3934/dcdsb.2012.17.2299info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:26:09Zoai:ri.conicet.gov.ar:11336/14879instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:26:10.204CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies
title A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies
spellingShingle A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies
Amster, Pablo Gustavo
Electro-Diffusion Models
Painlevé Ii
Unequal Valencies
title_short A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies
title_full A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies
title_fullStr A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies
title_full_unstemmed A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies
title_sort A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies
dc.creator.none.fl_str_mv Amster, Pablo Gustavo
Kwong, Man Kan
Rogers, Colin
author Amster, Pablo Gustavo
author_facet Amster, Pablo Gustavo
Kwong, Man Kan
Rogers, Colin
author_role author
author2 Kwong, Man Kan
Rogers, Colin
author2_role author
author
dc.subject.none.fl_str_mv Electro-Diffusion Models
Painlevé Ii
Unequal Valencies
topic Electro-Diffusion Models
Painlevé Ii
Unequal Valencies
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In prior work, a series of two-point boundary value problems have been investigated for a steady state two-ion electro-diffusion model system in which the sum of the valencies ν+ and ν− is zero. In that case, reduction is obtained to the canonical Painlevé II equation for the scaled electric field. Here, a physically important Neumann boundary value problem in the generic case when ν++ν−≠0 is investigated. The problem is novel in that the model equation for the electric field involves yet to be determined boundary values of the solution. A reduction of the Neumann boundary value problem in terms of elliptic functions is obtained for privileged valency ratios. A topological index argument is used to establish the existence of a solution in the general case, under the assumption ν++ν−≤0.
Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Kwong, Man Kan. Hong Kong Polytechnic University; China
Fil: Rogers, Colin. University Of New South Wales. Faculty Of Science; Australia. Hong Kong Polytechnic University; China
description In prior work, a series of two-point boundary value problems have been investigated for a steady state two-ion electro-diffusion model system in which the sum of the valencies ν+ and ν− is zero. In that case, reduction is obtained to the canonical Painlevé II equation for the scaled electric field. Here, a physically important Neumann boundary value problem in the generic case when ν++ν−≠0 is investigated. The problem is novel in that the model equation for the electric field involves yet to be determined boundary values of the solution. A reduction of the Neumann boundary value problem in terms of elliptic functions is obtained for privileged valency ratios. A topological index argument is used to establish the existence of a solution in the general case, under the assumption ν++ν−≤0.
publishDate 2012
dc.date.none.fl_str_mv 2012-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/14879
Amster, Pablo Gustavo; Kwong, Man Kan; Rogers, Colin; A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems-series B; 17; 7; 10-2012; 2299-2311
1531-3492
url http://hdl.handle.net/11336/14879
identifier_str_mv Amster, Pablo Gustavo; Kwong, Man Kan; Rogers, Colin; A Neumann Boundary Value Problem in Two-Ion Electro-diffusion with Unequal Valencies; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems-series B; 17; 7; 10-2012; 2299-2311
1531-3492
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://aimsciences.org/journals/displayArticlesnew.jsp?paperID=7475
info:eu-repo/semantics/altIdentifier/doi/10.3934/dcdsb.2012.17.2299
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Amer Inst Mathematical Sciences
publisher.none.fl_str_mv Amer Inst Mathematical Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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