{"id":113793,"date":"2013-05-02T00:00:00","date_gmt":"2013-05-02T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/null-control-and-measurable-sets\/"},"modified":"2013-05-02T00:00:00","modified_gmt":"2013-05-02T00:00:00","slug":"null-control-and-measurable-sets","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/ecuaciones-diferenciales-en-derivadas-parciales\/null-control-and-measurable-sets\/","title":{"rendered":"Null control and measurable sets"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jone Apraiz &#8212; <\/strong><\/h2>\n<p>El prop\u00f3sito de esta tesis es probar que es posible el control nulo de la ecuaci\u00f3n delcalor y el de otras evoluciones con coeficientes anal\u00edticos cuando las regiones donde seejerce el control son conjuntos medibles con medida positiva en el interior o en el bordedel dominio en que se desea controlar la temperatura inicial. Tambi\u00e9n obtenemos lasdesigualdades de observabilidad asociadas sobre dichos conjuntos medibles para laecuaci\u00f3n del calor. Las desigualdades de observabilidad obtenidas implican la existenciade controles admisibles acotados y ciertas propiedades bang-bang de los controlesadmisibles de tama\u00f1o acotado m\u00ednimo y para los de tiempo \u00f3ptimo de primera ysegunda clase (minimizar o retardar el tiempo de acci\u00f3n del control fijando su tama\u00f1o).<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Null control and measurable sets<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Null control and measurable sets <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jone Apraiz &#8212; <\/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 05\/02\/2013<\/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>Luis Escauriaza Zubiria<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: javier Duoandikoetxea zuazo <\/li>\n<li>enrique Fernandez cara (vocal)<\/li>\n<li>anna Doubova krasotchenko (vocal)<\/li>\n<li>Manuel Gonzalez burgos (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jone Apraiz &#8212; El prop\u00f3sito de esta tesis es probar que es posible el control nulo de [&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],"tags":[225836,7866,68970,225835,55393,150764],"class_list":["post-113793","post","type-post","status-publish","format-standard","hentry","category-ecuaciones-diferenciales-en-derivadas-parciales","category-pais-vasco-euskal-herriko-unibertsitatea","tag-anna-doubova-krasotchenko","tag-enrique-fernandez-cara","tag-javier-duoandikoetxea-zuazo","tag-jone-apraiz","tag-luis-escauriaza-zubiria","tag-manuel-gonzalez-burgos"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/113793","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=113793"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/113793\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=113793"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=113793"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=113793"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}