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dc.rights.licenseAtribución-NoComercial-SinDerivadas 4.0 Internacional
dc.contributor.advisorJiménez Urrea, Jose Manuel
dc.contributor.advisorChica Castaño, Cristian Camilo
dc.contributor.authorAgudelo Parra, Nelson Andrés
dc.date.accessioned2023-02-06T19:34:52Z
dc.date.available2023-02-06T19:34:52Z
dc.date.issued2022-09
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/83328
dc.description.abstractEn este trabajo estudiamos un problema semilineal que involucra un operador de tipo no local a través de la transformada de Fourier. Investigamos existencia y unicidad local de soluciones vía el principio de Duhamel y las propiedades del kernel asociado al operador involucrado. (Tomado de la fuente)
dc.description.abstractn this work we study a semilinear problem involving a type of non-local operator through the Fourier transform. We investigate the existence and local uniqueness of solutions, using Duhamel’s principle and the properties of the kernel associated with the aforementioned operator.
dc.format.extent86 páginas
dc.format.mimetypeapplication/pdf
dc.language.isospa
dc.publisherUniversidad Nacional de Colombia
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510 - Matemáticas
dc.subject.ddc510 - Matemáticas::515 - Análisis
dc.titleRepresentación integral de soluciones de problemas no locales
dc.typeTrabajo de grado - Maestría
dc.type.driverinfo:eu-repo/semantics/masterThesis
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.publisher.programMedellín - Ciencias - Maestría en Ciencias - Matemáticas
dc.contributor.researchgroupGrupo de investigación en matemáticas Universidad Nacional de Colombia Sede Medellín
dc.description.degreelevelMaestría
dc.description.degreenameMagíster en Ciencias - Matemáticas
dc.description.researchareaEcuaciones de evolución no lineales
dc.identifier.instnameUniversidad Nacional de Colombia
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourlhttps://repositorio.unal.edu.co/
dc.publisher.facultyFacultad de Ciencias
dc.publisher.placeMedellín, Colombia
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellín
dc.relation.indexedLaReferencia
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dc.relation.referencesD. Gilbarg and N. S. Trudinger. Elliptic Partial Differential Equations of Second Order, volume 224 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag. Berlin. Second edition, 1983.
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dc.relation.referencesF. Jones. Lebesgue integration on Euclidean space. Jones & Bartlett Learning, 2001.
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dc.relation.referencesG. Ponce and F. Linares. Introduction to Nonlinear Dispersive Equations. Universitext. Springer. New York, 2009.
dc.relation.referencesH. Brezis. Functional analysis, Sobolev spaces and partial differential equations. Springer Science & Business Media, 2010.
dc.relation.referencesJ. DRONIOU and C. IMBERT. Fractal First-Order Partial Differential Equations. Arch. Rational Mech. Anal. 182 (2006) 299-331. DOI: 10.1007/s00205-006-0429-2.
dc.relation.referencesJ. DRONIOU, G. THIERRY and J. VOVELLE. Global solution and smoothing effect for a non-local regularization of a hyperbolic equation. Article in Journal of Evolution Equations. August 2003. DOI: 10.1007/S00028-003-0503-1.
dc.relation.referencesJ. HEINONEN. Lectures on Lipschitz Analysis. Lectures at the 14th Jyväskylä Summer School in August 2004. http://www.math.jyu.fi/research/reports/rep100.pdf
dc.relation.referencesJ. Jiménez. Unique Continuation Properties for Some Nonlinear Dispersive Models. Tesis de Doctorado. Río de Janeiro, 2011.
dc.relation.referencesJ. Munkres. Analysis on manifolds. Westview Press, 1997.
dc.relation.referencesL. C. Evans. Partial differential equations. Graduate studies in mathematics. Ameri- can Mathematical Society, 1998.
dc.relation.referencesL. Grafakos. Classical Fourier analysis, volume 2. Springer, 2008.
dc.relation.referencesL. Fiske and C. Overturf. Tempered Distributions. University of New Me- xico, 2001. https://www.math.unm.edu/~crisp/courses/math402/spring16/ Distributions402CairnLionel.pdf
dc.relation.referencesL. Mattner. Complex differentiation under the integral. Department of Statistics. Univer- sity of Leeds. Leeds, LS2 9JT, England, 2001. http://www.nieuwarchief.nl/serie5/pdf/ naw5-2001-02-1-032.pdf
dc.relation.referencesR. Remmert. Theory of Complex Functions. Graduate Texts in Mathematics. Springer Scien- ce & Business Media, 1991.
dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.subject.lembFunciones de Kernel
dc.subject.lembTransformaciones de Fourier
dc.subject.proposalTransformada de Fourier
dc.subject.proposalFourier transform
dc.subject.proposalDuhamel’s principle
dc.subject.proposalweak solution
dc.subject.proposalPrincipio de Duhamel
dc.subject.proposalSolución débil
dc.subject.proposalWeak solution
dc.title.translatedIntegral representation of non local problems solutions
dc.type.coarhttp://purl.org/coar/resource_type/c_bdcc
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.contentText
dc.type.redcolhttp://purl.org/redcol/resource_type/TM
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2
oaire.awardtitleProblemas en ecuaciones diferenciales del tipo elíptico o dispersivo. Apoyo Ciencias 2021
oaire.fundernameFacultad de Ciencias sede Medellín
dcterms.audience.professionaldevelopmentInvestigadores
dc.description.curricularareaÁrea Curricular en Matemáticas


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Atribución-NoComercial-SinDerivadas 4.0 InternacionalEsta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial 4.0.Este documento ha sido depositado por parte de el(los) autor(es) bajo la siguiente constancia de depósito