A one-dimensional prescribed curvature equation modeling the corneal shape

Detalhes bibliográficos
Autor(a) principal: Coelho, Maria Isabel Esteves
Data de Publicação: 2014
Outros Autores: Corsato, Chiara, Omari, Pierpaolo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/4536
Resumo: We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.
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spelling A one-dimensional prescribed curvature equation modeling the corneal shapeMean curvature equationMixed boundary conditionPositive solutionExistenceUniquenessLinear stabilityOrder stabilityLyapunov stabilityLower and upper solutionsMonotone approximationTopological degreeWe prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.Springer International Publishing AGRCIPLCoelho, Maria Isabel EstevesCorsato, ChiaraOmari, Pierpaolo2015-05-14T10:58:38Z2014-052014-05-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/4536engCOELHO, Maria Isabel Esteves; CORSATO, Chiara; OMARI, Pierpaolo - A one-dimensional prescribed curvature equation modeling the corneal shape. Boundary Value Problems. (2014)1687-277010.1186/1687-2770-2014-127info: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:RCAAP2023-08-03T09:46:43Zoai:repositorio.ipl.pt:10400.21/4536Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:13:57.314342Repositório 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 A one-dimensional prescribed curvature equation modeling the corneal shape
title A one-dimensional prescribed curvature equation modeling the corneal shape
spellingShingle A one-dimensional prescribed curvature equation modeling the corneal shape
Coelho, Maria Isabel Esteves
Mean curvature equation
Mixed boundary condition
Positive solution
Existence
Uniqueness
Linear stability
Order stability
Lyapunov stability
Lower and upper solutions
Monotone approximation
Topological degree
title_short A one-dimensional prescribed curvature equation modeling the corneal shape
title_full A one-dimensional prescribed curvature equation modeling the corneal shape
title_fullStr A one-dimensional prescribed curvature equation modeling the corneal shape
title_full_unstemmed A one-dimensional prescribed curvature equation modeling the corneal shape
title_sort A one-dimensional prescribed curvature equation modeling the corneal shape
author Coelho, Maria Isabel Esteves
author_facet Coelho, Maria Isabel Esteves
Corsato, Chiara
Omari, Pierpaolo
author_role author
author2 Corsato, Chiara
Omari, Pierpaolo
author2_role author
author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Coelho, Maria Isabel Esteves
Corsato, Chiara
Omari, Pierpaolo
dc.subject.por.fl_str_mv Mean curvature equation
Mixed boundary condition
Positive solution
Existence
Uniqueness
Linear stability
Order stability
Lyapunov stability
Lower and upper solutions
Monotone approximation
Topological degree
topic Mean curvature equation
Mixed boundary condition
Positive solution
Existence
Uniqueness
Linear stability
Order stability
Lyapunov stability
Lower and upper solutions
Monotone approximation
Topological degree
description We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.
publishDate 2014
dc.date.none.fl_str_mv 2014-05
2014-05-01T00:00:00Z
2015-05-14T10:58:38Z
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/10400.21/4536
url http://hdl.handle.net/10400.21/4536
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv COELHO, Maria Isabel Esteves; CORSATO, Chiara; OMARI, Pierpaolo - A one-dimensional prescribed curvature equation modeling the corneal shape. Boundary Value Problems. (2014)
1687-2770
10.1186/1687-2770-2014-127
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 Springer International Publishing AG
publisher.none.fl_str_mv Springer International Publishing AG
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
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