{"id":54449,"date":"2006-06-09T00:00:00","date_gmt":"2006-06-09T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/metodos-espectrales-de-hermite-y-leyes-de-conservacion\/"},"modified":"2006-06-09T00:00:00","modified_gmt":"2006-06-09T00:00:00","slug":"metodos-espectrales-de-hermite-y-leyes-de-conservacion","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/resolucion-de-ecuaciones-diferenciales-en-derivadas-parciales\/metodos-espectrales-de-hermite-y-leyes-de-conservacion\/","title":{"rendered":"M\u00e9todos espectrales de hermite y leyes de conservaci\u00f3n"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Judith Rivas Ulloa <\/strong><\/h2>\n<p>La tesis que se presenta analiza m\u00e9todos espectrales basados en funciones de hermite aplicados a ecuaciones hiperb\u00f3licas escalares en una dimensi\u00f3n espacial, tanto lineales como no lineales, planteadas en toda la recta real. La idea de un m\u00e9todo espectral es aproximar la soluci\u00f3n exacta del problema dado mediante una combinaci\u00f3n lineal de las funciones de base, que en este trabajo son las funciones de hermite. El modo de calcular los coeficientes var\u00eda seg\u00fan el m\u00e9todo espectral considerado. Aqu\u00ed se estudian m\u00e9todos de galerkin y m\u00e9todos de colocaci\u00f3n pseudoespectrales.     en el caso de ecuaciones lineales, demostramos la convergencia de ambos m\u00e9todos en un espacio l2 con un peso adecuado del que las funciones de hermite forman una base ortogonal, con ayuda del teorema de equiValencia de lax-richmyer.     cuando se trata de ecuaciones no lineales, debido a que las soluciones  desarrollan discontinuidades, debemos introducir cierta cantidad de viscosidad para estabilizar el m\u00e9todo num\u00e9rico. Probamos la convergencia de los m\u00e9todos de viscosidad espectral hacia la \u00fanica soluci\u00f3n de entrop\u00eda, en espacios lp omega para cualquier p mayor i y cualquier omega subconjunto abierto y acotado de ir x (o,t). Para ello, utilizamos resultados de la teor\u00eda de compacidad por compensaci\u00f3n y medidas de young.     la posible falta de regularidad de las soluciones de ecuaciones hiperb\u00f3licas reduce la rapidez de convergencia de las aproximaciones espectrales. Por ello, hemos construido tambi\u00e9n un filtrado que aumenta el orden de convergencia. finalmente, hemos realizado experimentos num\u00e9ricos que corroboran los resultados te\u00f3ricos demostrados.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>M\u00e9todos espectrales de hermite y leyes de conservaci\u00f3n<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 M\u00e9todos espectrales de hermite y leyes de conservaci\u00f3n <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Judith Rivas Ulloa <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Pa\u00eds vasco\/euskal herriko unibertsitatea<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 06\/09\/2006<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Juli\u00e1n Aguirre Estib\u00e1lez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: enrique Zuazua iriondo <\/li>\n<li> Donat beneito rosa m. (vocal)<\/li>\n<li>otared Kavian (vocal)<\/li>\n<li>eduardo Casas renter\u00eda (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Judith Rivas Ulloa La tesis que se presenta analiza m\u00e9todos espectrales basados en funciones de hermite aplicados [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[3185,12909,1193],"tags":[120268,10857,24518,120267,113035,120269],"class_list":["post-54449","post","type-post","status-publish","format-standard","hentry","category-ecuaciones-diferenciales-en-derivadas-parciales","category-pais-vasco-euskal-herriko-unibertsitatea","category-resolucion-de-ecuaciones-diferenciales-en-derivadas-parciales","tag-donat-beneito-rosa-m","tag-eduardo-casas-renteria","tag-enrique-zuazua-iriondo","tag-judith-rivas-ulloa","tag-julian-aguirre-estibalez","tag-otared-kavian"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/54449","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=54449"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/54449\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=54449"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=54449"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=54449"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}