Ill posedness of a neural field equation with Heaviside firing rate function

We consider the initial value problem associated to the neural field equationut(x, t) = -u(x, t) + ZRm w(x, y) [1 + g(u(x, t) -u(y, t))] f(u(y, t)) dy, (x, t) Rm x (0, 1),where f is a Heaviside function, then we show that the problem is ill posed in Cb(Rm). The proof follows from a discontinuity arg...

Full description

Autores:: Cordero Ceballos, Juan Carlos
Pinilla Estupiñan, Ricardo

Tipo de recurso:: Article of journal

Fecha de publicación:: 2015

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

id	UNACIONAL2_2e7b518df7682672c79aa710f776858c
oai_identifier_str	oai:repositorio.unal.edu.co:unal/61887
network_acronym_str	UNACIONAL2
network_name_str	Universidad Nacional de Colombia
repository_id_str
spelling	Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cordero Ceballos, Juan Carlosb60a0ef4-a4b7-4817-a965-89881ea24eee300Pinilla Estupiñan, Ricardo79d4adc4-9867-4420-8c7b-3268eb793ad63002019-07-02T20:46:57Z2019-07-02T20:46:57Z2015-07-01ISSN: 2357-6529https://repositorio.unal.edu.co/handle/unal/61887http://bdigital.unal.edu.co/60699/We consider the initial value problem associated to the neural field equationut(x, t) = -u(x, t) + ZRm w(x, y) [1 + g(u(x, t) -u(y, t))] f(u(y, t)) dy, (x, t) Rm x (0, 1),where f is a Heaviside function, then we show that the problem is ill posed in Cb(Rm). The proof follows from a discontinuity argument apply to the equation's flow.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticashttps://revistas.unal.edu.co/index.php/bolma/article/view/54970Universidad Nacional de Colombia Revistas electrónicas UN Boletín de MatemáticasBoletín de MatemáticasCordero Ceballos, Juan Carlos and Pinilla Estupiñan, Ricardo (2015) Ill posedness of a neural field equation with Heaviside firing rate function. Boletín de Matemáticas, 22 (2). pp. 107-115. ISSN 2357-652951 Matemáticas / MathematicsNeural field equationring rate functionsynaptic and sensitive kernelwell and ill posednessflow of the equation.Ill posedness of a neural field equation with Heaviside firing rate functionArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL54970-278520-3-PB.pdfapplication/pdf350537https://repositorio.unal.edu.co/bitstream/unal/61887/1/54970-278520-3-PB.pdf62a3eb178efe5356a35b9676a855c7ddMD51THUMBNAIL54970-278520-3-PB.pdf.jpg54970-278520-3-PB.pdf.jpgGenerated Thumbnailimage/jpeg5501https://repositorio.unal.edu.co/bitstream/unal/61887/2/54970-278520-3-PB.pdf.jpgec34910562fe91254f84ca4f11bd23c6MD52unal/61887oai:repositorio.unal.edu.co:unal/618872024-04-20 23:26:17.399Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv	Ill posedness of a neural field equation with Heaviside firing rate function
title	Ill posedness of a neural field equation with Heaviside firing rate function
spellingShingle	Ill posedness of a neural field equation with Heaviside firing rate function 51 Matemáticas / Mathematics Neural field equation ring rate function synaptic and sensitive kernel well and ill posedness flow of the equation.
title_short	Ill posedness of a neural field equation with Heaviside firing rate function
title_full	Ill posedness of a neural field equation with Heaviside firing rate function
title_fullStr	Ill posedness of a neural field equation with Heaviside firing rate function
title_full_unstemmed	Ill posedness of a neural field equation with Heaviside firing rate function
title_sort	Ill posedness of a neural field equation with Heaviside firing rate function
dc.creator.fl_str_mv	Cordero Ceballos, Juan Carlos Pinilla Estupiñan, Ricardo
dc.contributor.author.spa.fl_str_mv	Cordero Ceballos, Juan Carlos Pinilla Estupiñan, Ricardo
dc.subject.ddc.spa.fl_str_mv	51 Matemáticas / Mathematics
topic	51 Matemáticas / Mathematics Neural field equation ring rate function synaptic and sensitive kernel well and ill posedness flow of the equation.
dc.subject.proposal.spa.fl_str_mv	Neural field equation ring rate function synaptic and sensitive kernel well and ill posedness flow of the equation.
description	We consider the initial value problem associated to the neural field equationut(x, t) = -u(x, t) + ZRm w(x, y) [1 + g(u(x, t) -u(y, t))] f(u(y, t)) dy, (x, t) Rm x (0, 1),where f is a Heaviside function, then we show that the problem is ill posed in Cb(Rm). The proof follows from a discontinuity argument apply to the equation's flow.
publishDate	2015
dc.date.issued.spa.fl_str_mv	2015-07-01
dc.date.accessioned.spa.fl_str_mv	2019-07-02T20:46:57Z
dc.date.available.spa.fl_str_mv	2019-07-02T20:46:57Z
dc.type.spa.fl_str_mv	Artículo de revista
dc.type.coar.fl_str_mv	http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/article
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/publishedVersion
dc.type.coar.spa.fl_str_mv	http://purl.org/coar/resource_type/c_6501
dc.type.coarversion.spa.fl_str_mv	http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.content.spa.fl_str_mv	Text
dc.type.redcol.spa.fl_str_mv	http://purl.org/redcol/resource_type/ART
format	http://purl.org/coar/resource_type/c_6501
status_str	publishedVersion
dc.identifier.issn.spa.fl_str_mv	ISSN: 2357-6529
dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/61887
dc.identifier.eprints.spa.fl_str_mv	http://bdigital.unal.edu.co/60699/
identifier_str_mv	ISSN: 2357-6529
url	https://repositorio.unal.edu.co/handle/unal/61887 http://bdigital.unal.edu.co/60699/
dc.language.iso.spa.fl_str_mv	spa
language	spa
dc.relation.spa.fl_str_mv	https://revistas.unal.edu.co/index.php/bolma/article/view/54970
dc.relation.ispartof.spa.fl_str_mv	Universidad Nacional de Colombia Revistas electrónicas UN Boletín de Matemáticas Boletín de Matemáticas
dc.relation.references.spa.fl_str_mv	Cordero Ceballos, Juan Carlos and Pinilla Estupiñan, Ricardo (2015) Ill posedness of a neural field equation with Heaviside firing rate function. Boletín de Matemáticas, 22 (2). pp. 107-115. ISSN 2357-6529
dc.rights.spa.fl_str_mv	Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv	http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv	Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv	http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv	info:eu-repo/semantics/openAccess
rights_invalid_str_mv	Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv	openAccess
dc.format.mimetype.spa.fl_str_mv	application/pdf
dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas
institution	Universidad Nacional de Colombia
bitstream.url.fl_str_mv	https://repositorio.unal.edu.co/bitstream/unal/61887/1/54970-278520-3-PB.pdf https://repositorio.unal.edu.co/bitstream/unal/61887/2/54970-278520-3-PB.pdf.jpg
bitstream.checksum.fl_str_mv	62a3eb178efe5356a35b9676a855c7dd ec34910562fe91254f84ca4f11bd23c6
bitstream.checksumAlgorithm.fl_str_mv	MD5 MD5
repository.name.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv	repositorio_nal@unal.edu.co
_version_	1814089765818990592

Ill posedness of a neural field equation with Heaviside firing rate function

Publicaciones similares