{"id":114911,"date":"2018-03-11T10:43:10","date_gmt":"2018-03-11T10:43:10","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/distance-of-attractors-of-evolutionary-equations-distancia-de-atractores-de-ecuaciones-de-evolucion\/"},"modified":"2018-03-11T10:43:10","modified_gmt":"2018-03-11T10:43:10","slug":"distance-of-attractors-of-evolutionary-equations-distancia-de-atractores-de-ecuaciones-de-evolucion","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/complutense-de-madrid\/distance-of-attractors-of-evolutionary-equations-distancia-de-atractores-de-ecuaciones-de-evolucion\/","title":{"rendered":"Distance of attractors of evolutionary equations.distancia de atractores de ecuaciones de evoluci\u00f3n."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Esperanza Santamar\u00eda Mart\u00edn <\/strong><\/h2>\n<p>This thesis\u00c2\u00a0is devoted\u00c2\u00a0to obtain\u00c2\u00a0good estimates\u00c2\u00a0of the distance\u00c2\u00a0of attractors\u00c2\u00a0once we know they behavecontinuously.\u00c2\u00a0our aim is to study\u00c2\u00a0what we have to ask to the system\u00c2\u00a0to improve\u00c2\u00a0the known\u00c2\u00a0rate ofconvergence\u00c2\u00a0of\u00c2\u00a0attractors\u00c2\u00a0existing\u00c2\u00a0in\u00c2\u00a0the\u00c2\u00a0literature.We\u00c2\u00a0have\u00c2\u00a0obtained\u00c2\u00a0that,\u00c2\u00a0if\u00c2\u00a0we\u00c2\u00a0have\u00c2\u00a0a\u00c2\u00a0finite\u00c2\u00a0dynamical\u00c2\u00a0system\u00c2\u00a0generated\u00c2\u00a0by\u00c2\u00a0a\u00c2\u00a0morse smale\u00c2\u00a0gradient\u00c2\u00a0mapwhich\u00c2\u00a0has\u00c2\u00a0an\u00c2\u00a0attractor\u00c2\u00a0and\u00c2\u00a0we\u00c2\u00a0perturb\u00c2\u00a0this\u00c2\u00a0system\u00c2\u00a0in\u00c2\u00a0such\u00c2\u00a0way\u00c2\u00a0so\u00c2\u00a0that\u00c2\u00a0the\u00c2\u00a0perturbed\u00c2\u00a0system\u00c2\u00a0has\u00c2\u00a0also\u00c2\u00a0anattractor,\u00c2\u00a0then\u00c2\u00a0the\u00c2\u00a0rate\u00c2\u00a0of\u00c2\u00a0convergence\u00c2\u00a0of\u00c2\u00a0these\u00c2\u00a0attractors\u00c2\u00a0is\u00c2\u00a0of\u00c2\u00a0order\u00c2\u00a0the\u00c2\u00a0distance\u00c2\u00a0of\u00c2\u00a0the\u00c2\u00a0corresponding\u00c2\u00a0time one\u00c2\u00a0maps.\u00c2\u00a0moreover,\u00c2\u00a0we\u00c2\u00a0generalize\u00c2\u00a0this\u00c2\u00a0result\u00c2\u00a0with\u00c2\u00a0the\u00c2\u00a0following\u00c2\u00a0one:\u00c2\u00a0if\u00c2\u00a0we\u00c2\u00a0have\u00c2\u00a0a\u00c2\u00a0finite\u00c2\u00a0dynamical\u00c2\u00a0systemgenerated\u00c2\u00a0by\u00c2\u00a0a\u00c2\u00a0morse smale\u00c2\u00a0gradient\u00c2\u00a0map\u00c2\u00a0which\u00c2\u00a0has\u00c2\u00a0an\u00c2\u00a0attractor,\u00c2\u00a0and\u00c2\u00a0we\u00c2\u00a0consider\u00c2\u00a0a\u00c2\u00a0non\u00c2\u00adautonomousperturbation\u00c2\u00a0of\u00c2\u00a0it,\u00c2\u00a0such\u00c2\u00a0that\u00c2\u00a0this\u00c2\u00a0non autonomous\u00c2\u00a0perturbed\u00c2\u00a0dynamical\u00c2\u00a0system\u00c2\u00a0has\u00c2\u00a0a\u00c2\u00a0pullback\u00c2\u00a0attractor,\u00c2\u00a0thenthe\u00c2\u00a0rate\u00c2\u00a0of\u00c2\u00a0convergence\u00c2\u00a0of\u00c2\u00a0the\u00c2\u00a0attractor\u00c2\u00a0and\u00c2\u00a0pullback\u00c2\u00a0attractor\u00c2\u00a0is\u00c2\u00a0of\u00c2\u00a0order\u00c2\u00a0the\u00c2\u00a0rate\u00c2\u00a0of\u00c2\u00a0convergence\u00c2\u00a0of\u00c2\u00a0thecorresponding\u00c2\u00a0time\u00c2\u00a0one\u00c2\u00a0maps.\u00c2\u00a0these\u00c2\u00a0results\u00c2\u00a0are\u00c2\u00a0obtained\u00c2\u00a0in\u00c2\u00a0a\u00c2\u00a0finite\u00c2\u00a0dimensional\u00c2\u00a0framework\u00c2\u00a0and\u00c2\u00a0the\u00c2\u00a0method of\u00c2\u00a0proof\u00c2\u00a0is\u00c2\u00a0using\u00c2\u00a0the\u00c2\u00a0shadowing\u00c2\u00a0properties\u00c2\u00a0that\u00c2\u00a0morse smale\u00c2\u00a0maps\u00c2\u00a0have.Since\u00c2\u00a0our\u00c2\u00a0framework\u00c2\u00a0for\u00c2\u00a0these\u00c2\u00a0results\u00c2\u00a0is\u00c2\u00a0finite\u00c2\u00a0dimensional,\u00c2\u00a0and\u00c2\u00a0we\u00c2\u00a0eventually\u00c2\u00a0want\u00c2\u00a0to\u00c2\u00a0apply\u00c2\u00a0thistechnique\u00c2\u00a0to\u00c2\u00a0infinite\u00c2\u00a0dimensional\u00c2\u00a0systems,\u00c2\u00a0we\u00c2\u00a0need\u00c2\u00a0a\u00c2\u00a0tool\u00c2\u00a0that\u00c2\u00a0reduces\u00c2\u00a0the\u00c2\u00a0system\u00c2\u00a0to\u00c2\u00a0a\u00c2\u00a0finite\u00c2\u00a0dimensionalone,\u00c2\u00a0inertial\u00c2\u00a0manifolds.\u00c2\u00a0these\u00c2\u00a0smooth\u00c2\u00a0finite\u00c2\u00a0dimensional\u00c2\u00a0manifolds,\u00c2\u00a0positive\u00c2\u00a0invariant\u00c2\u00a0under\u00c2\u00a0the\u00c2\u00a0flow\u00c2\u00a0andexponentially\u00c2\u00a0attractive,\u00c2\u00a0contain\u00c2\u00a0the\u00c2\u00a0attractor\u00c2\u00a0if\u00c2\u00a0the\u00c2\u00a0system\u00c2\u00a0has\u00c2\u00a0one.\u00c2\u00a0since\u00c2\u00a0we\u00c2\u00a0want\u00c2\u00a0to\u00c2\u00a0study\u00c2\u00a0the\u00c2\u00a0behavior\u00c2\u00a0of the\u00c2\u00a0systems\u00c2\u00a0under\u00c2\u00a0perturbations\u00c2\u00a0and\u00c2\u00a0obtain\u00c2\u00a0good\u00c2\u00a0rates\u00c2\u00a0for\u00c2\u00a0the\u00c2\u00a0convergence\u00c2\u00a0of\u00c2\u00a0the\u00c2\u00a0attractors,\u00c2\u00a0we\u00c2\u00a0study\u00c2\u00a0thebehavior\u00c2\u00a0of\u00c2\u00a0these\u00c2\u00a0inertial\u00c2\u00a0manifolds\u00c2\u00a0under\u00c2\u00a0perturbations\u00c2\u00a0of\u00c2\u00a0the\u00c2\u00a0system,\u00c2\u00a0providing\u00c2\u00a0good\u00c2\u00a0rates\u00c2\u00a0of\u00c2\u00a0itsconvergence\u00c2\u00a0in\u00c2\u00a0the\u00c2\u00a0c 0\u00c2\u00a0topology\u00c2\u00a0and\u00c2\u00a0also\u00c2\u00a0in\u00c2\u00a0the\u00c2\u00a0c 1\u00c2\u00a0topology.Finally,\u00c2\u00a0we\u00c2\u00a0apply\u00c2\u00a0the\u00c2\u00a0techniques\u00c2\u00a0mentioned\u00c2\u00a0above\u00c2\u00a0to\u00c2\u00a0address\u00c2\u00a0the\u00c2\u00a0problem\u00c2\u00a0of\u00c2\u00a0the\u00c2\u00a0distance\u00c2\u00a0ofattractors\u00c2\u00a0corresponding\u00c2\u00a0to\u00c2\u00a0a\u00c2\u00a0particular\u00c2\u00a0reaction\u00c2\u00a0diffusion\u00c2\u00a0equation\u00c2\u00a0and\u00c2\u00a0a\u00c2\u00a0perturbation\u00c2\u00a0of\u00c2\u00a0itdescribed\u00c2\u00a0in\u00c2\u00a0a\u00c2\u00a0thin\u00c2\u00a0domain.\u00c2\u00a0this\u00c2\u00a0thesis\u00c2\u00a0improves\u00c2\u00a0the\u00c2\u00a0rate\u00c2\u00a0of\u00c2\u00a0convergence\u00c2\u00a0of\u00c2\u00a0attractors\u00c2\u00a0for\u00c2\u00a0thisparticular\u00c2\u00a0problem\u00c2\u00a0existing\u00c2\u00a0in\u00c2\u00a0the\u00c2\u00a0literature.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Distance of attractors of evolutionary equations.distancia de atractores de ecuaciones de evoluci\u00f3n.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Distance of attractors of evolutionary equations.distancia de atractores de ecuaciones de evoluci\u00f3n. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Esperanza Santamar\u00eda Mart\u00edn <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Complutense de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 27\/11\/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>Jos\u00e9 Mar\u00eda Arrieta Algarra<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: an\u00edbal Rodr\u00edguez bernal <\/li>\n<li>alexandre Nolasco de carvalho (vocal)<\/li>\n<li>Jos\u00e9 Antonio Langa rosado (vocal)<\/li>\n<li>joan Sol\u00ed\u00a0-morales rubio (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Esperanza Santamar\u00eda Mart\u00edn This thesis\u00c2\u00a0is devoted\u00c2\u00a0to obtain\u00c2\u00a0good estimates\u00c2\u00a0of the distance\u00c2\u00a0of attractors\u00c2\u00a0once we know they behavecontinuously.\u00c2\u00a0our aim is [&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 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