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Representación integral de soluciones de problemas no locales
dc.rights.license | Atribución-NoComercial-SinDerivadas 4.0 Internacional |
dc.contributor.advisor | Jiménez Urrea, Jose Manuel |
dc.contributor.advisor | Chica Castaño, Cristian Camilo |
dc.contributor.author | Agudelo Parra, Nelson Andrés |
dc.date.accessioned | 2023-02-06T19:34:52Z |
dc.date.available | 2023-02-06T19:34:52Z |
dc.date.issued | 2022-09 |
dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/83328 |
dc.description.abstract | En 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.abstract | n 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.extent | 86 páginas |
dc.format.mimetype | application/pdf |
dc.language.iso | spa |
dc.publisher | Universidad Nacional de Colombia |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.subject.ddc | 510 - Matemáticas |
dc.subject.ddc | 510 - Matemáticas::515 - Análisis |
dc.title | Representación integral de soluciones de problemas no locales |
dc.type | Trabajo de grado - Maestría |
dc.type.driver | info:eu-repo/semantics/masterThesis |
dc.type.version | info:eu-repo/semantics/acceptedVersion |
dc.publisher.program | Medellín - Ciencias - Maestría en Ciencias - Matemáticas |
dc.contributor.researchgroup | Grupo de investigación en matemáticas Universidad Nacional de Colombia Sede Medellín |
dc.description.degreelevel | Maestría |
dc.description.degreename | Magíster en Ciencias - Matemáticas |
dc.description.researcharea | Ecuaciones de evolución no lineales |
dc.identifier.instname | Universidad Nacional de Colombia |
dc.identifier.reponame | Repositorio Institucional Universidad Nacional de Colombia |
dc.identifier.repourl | https://repositorio.unal.edu.co/ |
dc.publisher.faculty | Facultad de Ciencias |
dc.publisher.place | Medellín, Colombia |
dc.publisher.branch | Universidad Nacional de Colombia - Sede Medellín |
dc.relation.indexed | LaReferencia |
dc.relation.references | B. P. Palka. An introduction to Complex Function Theory . Undergraduate Texts in Mathe- matics. Springer, 2012. |
dc.relation.references | C. Bucur and E. Valdinoci. Nonlocal Diffusion and Applications. Lecture Notes of the Unione Matematica Italiana. Springer, 2015. |
dc.relation.references | C. Chica. Some aspects of the obstacle problem. Tesis de maestría. Medellín, 2020. |
dc.relation.references | C. IMBERT. A non-local regularization of first order Hamilton-Jacobi equations. Journal of Differential Equations, Elsevier, 2005, 211 (1), pp.218-246. 10.1016/j.jde.2004.06.001. hal- 00176542 |
dc.relation.references | C. Zuily. Éléments de distributions et d’équations aux dérivées partielles. Cours et problèmes résolus. Donud, París, 2002. ISBN 2 10 005735 9. |
dc.relation.references | D. 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. |
dc.relation.references | D. Restrepo. On the fractional Laplacian and non local operators. Tesis de maestría. Mede- llín, 2018. |
dc.relation.references | E. JAKOEBSEN and K. KARLSEN. A maximum principle for semicontinuous function applicable to integro-partial differential equations. Prepint |
dc.relation.references | F. Jones. Lebesgue integration on Euclidean space. Jones & Bartlett Learning, 2001. |
dc.relation.references | G B. Folland. Higher-Order Derivatives and Taylor’s Formula in Several Variables. https: //sites.math.washington.edu/~folland/Math425/taylor2.pdf |
dc.relation.references | G. Ponce and F. Linares. Introduction to Nonlinear Dispersive Equations. Universitext. Springer. New York, 2009. |
dc.relation.references | H. Brezis. Functional analysis, Sobolev spaces and partial differential equations. Springer Science & Business Media, 2010. |
dc.relation.references | J. 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.references | J. 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.references | J. 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.references | J. Jiménez. Unique Continuation Properties for Some Nonlinear Dispersive Models. Tesis de Doctorado. Río de Janeiro, 2011. |
dc.relation.references | J. Munkres. Analysis on manifolds. Westview Press, 1997. |
dc.relation.references | L. C. Evans. Partial differential equations. Graduate studies in mathematics. Ameri- can Mathematical Society, 1998. |
dc.relation.references | L. Grafakos. Classical Fourier analysis, volume 2. Springer, 2008. |
dc.relation.references | L. 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.references | L. 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.references | R. Remmert. Theory of Complex Functions. Graduate Texts in Mathematics. Springer Scien- ce & Business Media, 1991. |
dc.rights.accessrights | info:eu-repo/semantics/openAccess |
dc.subject.lemb | Funciones de Kernel |
dc.subject.lemb | Transformaciones de Fourier |
dc.subject.proposal | Transformada de Fourier |
dc.subject.proposal | Fourier transform |
dc.subject.proposal | Duhamel’s principle |
dc.subject.proposal | weak solution |
dc.subject.proposal | Principio de Duhamel |
dc.subject.proposal | Solución débil |
dc.subject.proposal | Weak solution |
dc.title.translated | Integral representation of non local problems solutions |
dc.type.coar | http://purl.org/coar/resource_type/c_bdcc |
dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa |
dc.type.content | Text |
dc.type.redcol | http://purl.org/redcol/resource_type/TM |
oaire.accessrights | http://purl.org/coar/access_right/c_abf2 |
oaire.awardtitle | Problemas en ecuaciones diferenciales del tipo elíptico o dispersivo. Apoyo Ciencias 2021 |
oaire.fundername | Facultad de Ciencias sede Medellín |
dcterms.audience.professionaldevelopment | Investigadores |
dc.description.curriculararea | Área Curricular en Matemáticas |
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