Constructing solutions for a kinetic model of angiogenesis in annular domains

We present an iterative technique to construct stable solutions for an angiogenesis model set in an annular region. Branching, anastomosis and extension of blood vessel tips is described by an integrodifferential kinetic equation of Fokker-Planck type supplemented with nonlocal boundary conditions a...

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Detalles Bibliográficos
Autores: Carpio Rodríguez, Ana María, Duro, Gema, Negreanu Pruna, Mihaela
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/18799
Acceso en línea:https://hdl.handle.net/20.500.14352/18799
Access Level:acceso abierto
Palabra clave:519.8
Angiogenesis
Integrodifferential model
Kinetic-diffusion equations
Fokker–Planck operator
Bounded domains
Nonlocal and Neumann boundary conditions
Ecuaciones diferenciales
Investigación operativa (Matemáticas)
Sistema cardiovascular
1202.07 Ecuaciones en Diferencias
1207 Investigación Operativa
2411.03 Fisiología Cardiovascular
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oai_identifier_str oai:docta.ucm.es:20.500.14352/18799
network_acronym_str ES
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repository_id_str
spelling Constructing solutions for a kinetic model of angiogenesis in annular domainsCarpio Rodríguez, Ana MaríaDuro, GemaNegreanu Pruna, Mihaela519.8AngiogenesisIntegrodifferential modelKinetic-diffusion equationsFokker–Planck operatorBounded domainsNonlocal and Neumann boundary conditionsEcuaciones diferencialesInvestigación operativa (Matemáticas)Sistema cardiovascular1202.07 Ecuaciones en Diferencias1207 Investigación Operativa2411.03 Fisiología CardiovascularWe present an iterative technique to construct stable solutions for an angiogenesis model set in an annular region. Branching, anastomosis and extension of blood vessel tips is described by an integrodifferential kinetic equation of Fokker-Planck type supplemented with nonlocal boundary conditions and coupled to a diffusion problem with Neumann boundary conditions through the force field created by the tumor induced angiogenic factor and the flux of vessel tips. Convergence proofs exploit balance equations, estimates of velocity decay and compactness results for kinetic operators, combined with gradient estimates of heat kernels for Neumann problems in non convex domains.ElsevierUniversidad Complutense de Madrid20172017-05-0120172017-05-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/18799reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/187992026-06-02T12:44:21Z
dc.title.none.fl_str_mv Constructing solutions for a kinetic model of angiogenesis in annular domains
title Constructing solutions for a kinetic model of angiogenesis in annular domains
spellingShingle Constructing solutions for a kinetic model of angiogenesis in annular domains
Carpio Rodríguez, Ana María
519.8
Angiogenesis
Integrodifferential model
Kinetic-diffusion equations
Fokker–Planck operator
Bounded domains
Nonlocal and Neumann boundary conditions
Ecuaciones diferenciales
Investigación operativa (Matemáticas)
Sistema cardiovascular
1202.07 Ecuaciones en Diferencias
1207 Investigación Operativa
2411.03 Fisiología Cardiovascular
title_short Constructing solutions for a kinetic model of angiogenesis in annular domains
title_full Constructing solutions for a kinetic model of angiogenesis in annular domains
title_fullStr Constructing solutions for a kinetic model of angiogenesis in annular domains
title_full_unstemmed Constructing solutions for a kinetic model of angiogenesis in annular domains
title_sort Constructing solutions for a kinetic model of angiogenesis in annular domains
dc.creator.none.fl_str_mv Carpio Rodríguez, Ana María
Duro, Gema
Negreanu Pruna, Mihaela
author Carpio Rodríguez, Ana María
author_facet Carpio Rodríguez, Ana María
Duro, Gema
Negreanu Pruna, Mihaela
author_role author
author2 Duro, Gema
Negreanu Pruna, Mihaela
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 519.8
Angiogenesis
Integrodifferential model
Kinetic-diffusion equations
Fokker–Planck operator
Bounded domains
Nonlocal and Neumann boundary conditions
Ecuaciones diferenciales
Investigación operativa (Matemáticas)
Sistema cardiovascular
1202.07 Ecuaciones en Diferencias
1207 Investigación Operativa
2411.03 Fisiología Cardiovascular
topic 519.8
Angiogenesis
Integrodifferential model
Kinetic-diffusion equations
Fokker–Planck operator
Bounded domains
Nonlocal and Neumann boundary conditions
Ecuaciones diferenciales
Investigación operativa (Matemáticas)
Sistema cardiovascular
1202.07 Ecuaciones en Diferencias
1207 Investigación Operativa
2411.03 Fisiología Cardiovascular
description We present an iterative technique to construct stable solutions for an angiogenesis model set in an annular region. Branching, anastomosis and extension of blood vessel tips is described by an integrodifferential kinetic equation of Fokker-Planck type supplemented with nonlocal boundary conditions and coupled to a diffusion problem with Neumann boundary conditions through the force field created by the tumor induced angiogenic factor and the flux of vessel tips. Convergence proofs exploit balance equations, estimates of velocity decay and compactness results for kinetic operators, combined with gradient estimates of heat kernels for Neumann problems in non convex domains.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-05-01
2017
2017-05-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/18799
url https://hdl.handle.net/20.500.14352/18799
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869420115734298624
score 15,300719

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