{"id":86266,"date":"2000-08-09T00:00:00","date_gmt":"2000-08-09T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/las-soluciones-periodicas-de-una-ecuacion-de-la-cuerda-vibrante-con-disipacion\/"},"modified":"2000-08-09T00:00:00","modified_gmt":"2000-08-09T00:00:00","slug":"las-soluciones-periodicas-de-una-ecuacion-de-la-cuerda-vibrante-con-disipacion","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/las-soluciones-periodicas-de-una-ecuacion-de-la-cuerda-vibrante-con-disipacion\/","title":{"rendered":"Las soluciones peri\u00f3dicas de una ecuaci\u00f3n de la cuerda vibrante con disipaci\u00f3n"},"content":{"rendered":"<h2>Tesis doctoral de <strong>  Robles P\u00e9rez Aureliano Mat\u00edas <\/strong><\/h2>\n<p>En la presente tesis se hace un estudio de la ecuaci\u00f3n de sine-gordon forzada y con rozamiento,  utt(t,x)-uxx(t,x)+cut(t,x)+a sin u (t,x)=f(t,x)  m\u00e1s concretamente,se establecen resultados referentes a las soluciones peri\u00f3dicas(en las dos variables) de esta ecuaci\u00f3n. Para ello se utilizan el m\u00e9todo de sub y super-soluciones y la teor\u00eda de grado. El objetivo es generalizar varios resultados conocidos para las soluciones peri\u00f3dicas de la ecuaci\u00f3n del p\u00e9ndulo forzado,  x\u00bb\u00bb(t)+cx\u00c2\u00bf(t)+a sin x(t)=f(t)  se divide la tesis en tres cap\u00edtulos. En el primero se establece como resultado principal un principio del m\u00e1ximo para las soluciones peri\u00f3dicas de la ecuaci\u00f3n del tel\u00e9grafo,  utt-uxx-cut+lamda u=f(t,x)  a partir detal principio se justifica la utilizaci\u00f3n del metodo de sub y super-soluciones.  en el segundo cap\u00edtulo se usan dos definiciones de \u00edndice para las soluciones peri\u00f3dicas y aisladas de la ecuaci\u00f3n de evoluci\u00f3n dada por  \u00ed\u00bc+c\u00ed\u00bc+lu=f(t,u)  donde l es un operador lineal, autoadjunto, no acotado y coercivo. Como resultado principal, se establece la equiValencia de las dos definiciones. para poder establecer tal equiValencia se hace uso de la clase de operadores de tipo alfa-contractivo. Adem\u00e1s, se obtiene una condici\u00f3n necesaria para tener soluciones asint\u00f3ticamente estables.  en el tercer cap\u00edtulo se utilizan las herramientas construidas en los dos anteriores para obtener resultados de existencia de soluciones peri\u00f3dicas (aplicaci\u00f3n del m\u00e9todo de sub y super-soluciones) y sobre multiplicidad e inestabilidad de tales soluciones(aplicaciones de la teor\u00eda de grado).<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Las soluciones peri\u00f3dicas de una ecuaci\u00f3n de la cuerda vibrante con disipaci\u00f3n<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Las soluciones peri\u00f3dicas de una ecuaci\u00f3n de la cuerda vibrante con disipaci\u00f3n <\/li>\n<li><strong>Autor:<\/strong>\u00a0  Robles P\u00e9rez Aureliano Mat\u00edas <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Granada<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 08\/09\/2000<\/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>Rafael Ortega R\u00edos<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: jean Mawhin <\/li>\n<li>Juli\u00e1n Lopez gomez (vocal)<\/li>\n<li>r. Ward james (vocal)<\/li>\n<li> Sabina de lis Jos\u00e9 claudio (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Robles P\u00e9rez Aureliano Mat\u00edas En la presente tesis se hace un estudio de la ecuaci\u00f3n de sine-gordon [&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":[3183,3185,126],"tags":[15087,36486,181178,32613,181177,36488],"class_list":["post-86266","post","type-post","status-publish","format-standard","hentry","category-analisis-y-analisis-funcional","category-ecuaciones-diferenciales-en-derivadas-parciales","category-matematicas","tag-jean-mawhin","tag-julian-lopez-gomez","tag-r-ward-james","tag-rafael-ortega-rios","tag-robles-perez-aureliano-matias","tag-sabina-de-lis-jose-claudio"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/86266","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=86266"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/86266\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=86266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=86266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=86266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}