Rotating spirals in segregated reaction-diffusion systems

Autores
Salort, Ariel Martin; Terracini, Susanna; Verzini, Gianmaria; Zilio, Alessandro
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give a complete characterization of the boundary traces ϕi(i = 1, . . . , K) supporting spiraling waves, rotating with a given angular speed ω, which appear as singular limits ofcompetition-diffusion systems of the type∂tui − ∆ui = µui − βui ∑j6=iaijujin Ω × R+ui = ϕi on ∂Ω × R+ui(x, 0) = ui,0(x) for x ∈ Ωas β → +∞. Here Ω is a rotationally invariant planar set and aij > 0 for every i and j. We tacklealso the homogeneous Dirichlet and Neumann boundary conditions, as well as entire solutionsin the plane. As a byproduct of our analysis we detect explicit families of eternal, entire solutionsof the pure heat equation, parameterized by ω ∈ R, which reduce to homogeneous harmonicpolynomials for ω = 0.
Fil: Salort, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: Terracini, Susanna. Università di Torino; Italia
Fil: Verzini, Gianmaria. Università degli Studi di Milano; Italia
Fil: Zilio, Alessandro. Universite de Paris 1 - Pantheon Sorbonne.; Francia
Materia
COMPETITION-DIFFUSION SYSTEMS
SINGULAR PERTURBATION
FREE BOUNDARY PROBLEMS
SPIRAL WAWES
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:11336/291515
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/291515
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Rotating spirals in segregated reaction-diffusion systemsSalort, Ariel MartinTerracini, SusannaVerzini, GianmariaZilio, AlessandroCOMPETITION-DIFFUSION SYSTEMSSINGULAR PERTURBATIONFREE BOUNDARY PROBLEMSSPIRAL WAWEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a complete characterization of the boundary traces ϕi(i = 1, . . . , K) supporting spiraling waves, rotating with a given angular speed ω, which appear as singular limits ofcompetition-diffusion systems of the type∂tui − ∆ui = µui − βui ∑j6=iaijujin Ω × R+ui = ϕi on ∂Ω × R+ui(x, 0) = ui,0(x) for x ∈ Ωas β → +∞. Here Ω is a rotationally invariant planar set and aij > 0 for every i and j. We tacklealso the homogeneous Dirichlet and Neumann boundary conditions, as well as entire solutionsin the plane. As a byproduct of our analysis we detect explicit families of eternal, entire solutionsof the pure heat equation, parameterized by ω ∈ R, which reduce to homogeneous harmonicpolynomials for ω = 0.Fil: Salort, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: Terracini, Susanna. Università di Torino; ItaliaFil: Verzini, Gianmaria. Università degli Studi di Milano; ItaliaFil: Zilio, Alessandro. Universite de Paris 1 - Pantheon Sorbonne.; FranciaMathematical Sciences Publishers2025-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/291515Salort, Ariel Martin; Terracini, Susanna; Verzini, Gianmaria; Zilio, Alessandro; Rotating spirals in segregated reaction-diffusion systems; Mathematical Sciences Publishers; Analysis & PDE; 18; 3; 3-2025; 549-5901948-206XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://msp.org/apde/2025/18-3/p01.xhtmlinfo:eu-repo/semantics/altIdentifier/doi/10.2140/apde.2025.18.549info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-08-25T14:44:59Zoai:ri.conicet.gov.ar:11336/291515instacron: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:34982026-08-25 14:44:59.347CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Rotating spirals in segregated reaction-diffusion systems
title Rotating spirals in segregated reaction-diffusion systems
spellingShingle Rotating spirals in segregated reaction-diffusion systems
Salort, Ariel Martin
COMPETITION-DIFFUSION SYSTEMS
SINGULAR PERTURBATION
FREE BOUNDARY PROBLEMS
SPIRAL WAWES
title_short Rotating spirals in segregated reaction-diffusion systems
title_full Rotating spirals in segregated reaction-diffusion systems
title_fullStr Rotating spirals in segregated reaction-diffusion systems
title_full_unstemmed Rotating spirals in segregated reaction-diffusion systems
title_sort Rotating spirals in segregated reaction-diffusion systems
dc.creator.none.fl_str_mv Salort, Ariel Martin
Terracini, Susanna
Verzini, Gianmaria
Zilio, Alessandro
author Salort, Ariel Martin
author_facet Salort, Ariel Martin
Terracini, Susanna
Verzini, Gianmaria
Zilio, Alessandro
author_role author
author2 Terracini, Susanna
Verzini, Gianmaria
Zilio, Alessandro
author2_role author
author
author
dc.subject.none.fl_str_mv COMPETITION-DIFFUSION SYSTEMS
SINGULAR PERTURBATION
FREE BOUNDARY PROBLEMS
SPIRAL WAWES
topic COMPETITION-DIFFUSION SYSTEMS
SINGULAR PERTURBATION
FREE BOUNDARY PROBLEMS
SPIRAL WAWES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We give a complete characterization of the boundary traces ϕi(i = 1, . . . , K) supporting spiraling waves, rotating with a given angular speed ω, which appear as singular limits ofcompetition-diffusion systems of the type∂tui − ∆ui = µui − βui ∑j6=iaijujin Ω × R+ui = ϕi on ∂Ω × R+ui(x, 0) = ui,0(x) for x ∈ Ωas β → +∞. Here Ω is a rotationally invariant planar set and aij > 0 for every i and j. We tacklealso the homogeneous Dirichlet and Neumann boundary conditions, as well as entire solutionsin the plane. As a byproduct of our analysis we detect explicit families of eternal, entire solutionsof the pure heat equation, parameterized by ω ∈ R, which reduce to homogeneous harmonicpolynomials for ω = 0.
Fil: Salort, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: Terracini, Susanna. Università di Torino; Italia
Fil: Verzini, Gianmaria. Università degli Studi di Milano; Italia
Fil: Zilio, Alessandro. Universite de Paris 1 - Pantheon Sorbonne.; Francia
description We give a complete characterization of the boundary traces ϕi(i = 1, . . . , K) supporting spiraling waves, rotating with a given angular speed ω, which appear as singular limits ofcompetition-diffusion systems of the type∂tui − ∆ui = µui − βui ∑j6=iaijujin Ω × R+ui = ϕi on ∂Ω × R+ui(x, 0) = ui,0(x) for x ∈ Ωas β → +∞. Here Ω is a rotationally invariant planar set and aij > 0 for every i and j. We tacklealso the homogeneous Dirichlet and Neumann boundary conditions, as well as entire solutionsin the plane. As a byproduct of our analysis we detect explicit families of eternal, entire solutionsof the pure heat equation, parameterized by ω ∈ R, which reduce to homogeneous harmonicpolynomials for ω = 0.
publishDate 2025
dc.date.none.fl_str_mv 2025-03
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/11336/291515
Salort, Ariel Martin; Terracini, Susanna; Verzini, Gianmaria; Zilio, Alessandro; Rotating spirals in segregated reaction-diffusion systems; Mathematical Sciences Publishers; Analysis & PDE; 18; 3; 3-2025; 549-590
1948-206X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/291515
identifier_str_mv Salort, Ariel Martin; Terracini, Susanna; Verzini, Gianmaria; Zilio, Alessandro; Rotating spirals in segregated reaction-diffusion systems; Mathematical Sciences Publishers; Analysis & PDE; 18; 3; 3-2025; 549-590
1948-206X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://msp.org/apde/2025/18-3/p01.xhtml
info:eu-repo/semantics/altIdentifier/doi/10.2140/apde.2025.18.549
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
application/pdf
dc.publisher.none.fl_str_mv Mathematical Sciences Publishers
publisher.none.fl_str_mv Mathematical Sciences Publishers
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 13.24418

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