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Análisis teórico de un modelo de deflexión de placas

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dc.contributor.advisorBanquet Brango, Carlos Albertospa
dc.contributor.advisorVillamizar Roa, Élder Jesússpa
dc.contributor.authorCorpa Liñan, Luis Enrique
dc.date.accessioned2022-09-01T19:53:29Z
dc.date.available2023-09-01
dc.date.available2022-09-01T19:53:29Z
dc.date.issued2022-09-01
dc.description.abstractThis thesis is devoted to the study of the initial value problem for a nonlinear plate equation in Rn × (0, ∞) with initial data in Modulation spaces, which includes the Bessel-potential Hs p and Besov B s p,q spaces, for large enought regularity index s. We derive a set of time-decay estimates for the corresponding linear plate equation on the framework of modulation spaces, and then, we use these results to analyze the existence and asymptotic stability of global solutions of the nonlinear problem.eng
dc.description.degreelevelMaestríaspa
dc.description.degreenameMagister en Matemáticasspa
dc.description.modalityTrabajos de Investigación y/o Extensiónspa
dc.description.resumenEste trabajo está dedicado al estudio de un problema de valor inicial para una ecuación no lineal de placas en $\mathbb{R}^{n} \times (0,\infty)$ con datos iniciales en espacios de modulación, que incluye el espacio de potenciales de Bessel $H^{s}_{p}$ y espacios de Besov $B^{s}_{p,q}$, para índices de regularidad $s$ suficientemente grande. Derivamos un conjunto de estimaciones de decaimiento en tiempo para la ecuación de placa lineal correspondiente en el marco de los espacios de modulación, y luego usamos estos resultados para analizar la existencia y la estabilidad asintótica de las soluciones globales del problema no lineal.spa
dc.description.tableofcontentsDeclaración de Autoría ............................................................................................................................................................................................................................................. Vspa
dc.description.tableofcontentsResumen ......................................................................................................................................................................................................................................................................... VIIspa
dc.description.tableofcontentsAgradecimientos ......................................................................................................................................................................................................................................................... XIspa
dc.description.tableofcontentsINTRODUCCIÓN ............................................................................................................................................................................................................................................................. 1spa
dc.description.tableofcontents1. PRELIMINARES .......................................................................................................................................................................................................................................................... 5spa
dc.description.tableofcontents1.1. Lemas técnicos ........................................................................................................................................................................................................................................................ 5spa
dc.description.tableofcontents1.2. Espacios $L^p$ ...................................................................................................................................................................................................................................................... 11spa
dc.description.tableofcontents1.3. Transformada de Föurier ............................................................................................................................................................................................................................... 13spa
dc.description.tableofcontents1.4. Espacio de Schwartz ........................................................................................................................................................................................................................................ 17spa
dc.description.tableofcontents1.5. Transformada de Föurier en $L^2$ ....................................................................................................................................................................................................... 20spa
dc.description.tableofcontents1.6. Distribuciones temperadas .......................................................................................................................................................................................................................... 21spa
dc.description.tableofcontents1.7. Espacios de Sobolev ......................................................................................................................................................................................................................................... 24spa
dc.description.tableofcontents1.8. Espacios de modulación .............................................................................................................................................................................................................................. 29spa
dc.description.tableofcontents2. ESTIMATIVAS DE DECAIMIENTO ............................................................................................................................................................................................................... 39spa
dc.description.tableofcontents2.1. Planteamiento del problema .................................................................................................................................................................................................................... 39spa
dc.description.tableofcontents2.2. Estimativas de decaimiento en $L^{\infty}$ y $H^s_p$ ......................................................................................................................................................... 40spa
dc.description.tableofcontents2.3. Estimativas de decaimiento en $M^s_{p,q}$ .................................................................................................................................................................................. 51spa
dc.description.tableofcontents2.3.1. Estimativa de $\Vert \Lambda_{\theta,\frac{1}{2}}(t) g \Vert_{M^s_{p,q}}$ ................................................................................................................. 52spa
dc.description.tableofcontents2.3.2. Estimativa de $\Vert \partial_t \Lambda_{\theta,1}(t) g \Vert_{M^{s-1}_{p,q}}$ ...................................................................................................... 57spa
dc.description.tableofcontents2.3.3. Estimativa de $\Vert \partial_t S(t) u_0 \Vert_{M^{s}_{p,q}}$ ............................................................................................................................................ 60spa
dc.description.tableofcontents2.3.4. Estimativa de $\Vert \partial_t^2 S(t) u_0 \Vert_{M^{s-1}_{p,q}}$ ................................................................................................................................... 63spa
dc.description.tableofcontents2.3.5. Estimativa de $\Vert S(t) \Delta u_1 \Vert_{M^{s}_{p,q}}$ ..................................................................................................................................................... 66spa
dc.description.tableofcontents2.3.6. Estimativa de $\Vert \partial_t S(t) \Delta u_1 \Vert_{M^{s-1}_{p,q}}$ ........................................................................................................................... 67spa
dc.description.tableofcontents3. RESULTADOS DE EXISTENCIA ..................................................................................................................................................................................................................... 68spa
dc.description.tableofcontents3.1. Espacios de solución ....................................................................................................................................................................................................................................... 68spa
dc.description.tableofcontents3.2. Estimativas de no linealidad en espacios de Modulación .................................................................................................................................................... 68spa
dc.description.tableofcontents3.3. Existencia de soluciones locales y globales en espacios de Modulación ................................................................................................................... 76spa
dc.description.tableofcontents4. DISPERSIÓN Y ESTABILIDAD ASÍNTOTICA ........................................................................................................................................................................................ 83spa
dc.description.tableofcontents5. CONCLUSIONES ................................................................................................................................................................................................................................................... 88spa
dc.description.tableofcontents5.1. Conclusiones ......................................................................................................................................................................................................................................................... 88spa
dc.description.tableofcontents5.2. Trabajos futuros ................................................................................................................................................................................................................................................. 88spa
dc.description.tableofcontentsBibliografía ..................................................................................................................................................................................................................................................................... 89spa
dc.format.mimetypeapplication/pdfspa
dc.identifier.urihttps://repositorio.unicordoba.edu.co/handle/ucordoba/6508
dc.language.isospaspa
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.publisher.placeMontería, Córdoba, Colombiaspa
dc.publisher.programMaestría en Matemáticasspa
dc.rightsCopyright Universidad de Córdoba, 2022spa
dc.rights.accessrightsinfo:eu-repo/semantics/embargoedAccessspa
dc.rights.creativecommonsAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)spa
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/spa
dc.subject.keywordsPlate equationseng
dc.subject.keywordsModulation spaces,eng
dc.subject.keywordsTime-decay estimates,eng
dc.subject.keywordsGlobal solutionseng
dc.subject.keywordsStabilityeng
dc.subject.proposalEcuación de placasspa
dc.subject.proposalEspacios de modulaciónspa
dc.subject.proposalEstimativas de decaimiento en tiempospa
dc.subject.proposalSolución globalspa
dc.subject.proposalEstabilidadspa
dc.titleAnálisis teórico de un modelo de deflexión de placasspa
dc.typeTrabajo de grado - Maestríaspa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdccspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/masterThesisspa
dc.type.redcolhttps://purl.org/redcol/resource_type/TMspa
dc.type.versioninfo:eu-repo/semantics/submittedVersionspa
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