{"id":41512,"date":"1999-01-01T00:00:00","date_gmt":"1999-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/comportamiento-asintotico-de-ecuaciones-de-difusion-y-conveccion-no-lineales\/"},"modified":"1999-01-01T00:00:00","modified_gmt":"1999-01-01T00:00:00","slug":"comportamiento-asintotico-de-ecuaciones-de-difusion-y-conveccion-no-lineales","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/comportamiento-asintotico-de-ecuaciones-de-difusion-y-conveccion-no-lineales\/","title":{"rendered":"Comportamiento asintotico de ecuaciones de difusion y conveccion no lineales."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Guillermo Reyes Souto <\/strong><\/h2>\n<p>En este tesis se aborda el estudio de comportamiento asint\u00f3tico para tiempos grandes de las soluciones del problema de cauchy para la ecuaci\u00f3n  u sub t = delta u elevado m &#8211; (u elevado q) sub x sub 1  con m &gt; 1 y datos iniciales en l elevado 1, extendiendo resultados anteriores para el caso de difusi\u00f3n lineal (es decir, m = 1). Se demuestra que el comportamiento asnt\u00f3tico depende de la relaci\u00f3n entre los exponentes m y q. si q &gt; m + 1\/n (n es la dimensi\u00f3n), hay un fen\u00f3meno de simplificaci\u00f3n asint\u00f3tica hacia la ecuaci\u00f3n del medio poroso, y el comportamiento asint\u00f3tico viene dado por las soluciones fundamentales de dicha ecuaci\u00f3n, mientras que si q = m + 1\/n, no hay simplificaci\u00f3n y el comportamiento asnt\u00f3tico se describe en t\u00e9rminos de las \u00fanicas soluciones fundamentales autosemejantes de la ecuaci\u00f3n original.  tambi\u00e9n se estudia un caso de asint\u00f3tica \u00abcontra\u00edda\u00bb, concretamente se considera la ecuaci\u00f3n de primer orden:  u sub t + (u elevado m) sub x + u elevado p = 0  para el valor cr\u00edtico del exponente de absorci\u00f3n p = m + 1, y se estudia el comportamiento asint\u00f3tico de las soluciones acotadas de soporte compacto, obteni\u00e9ndose como perfil asint\u00f3tico una versi\u00f3n contra\u00edda de una de las soluciones fundamentales de la ley de conservaci\u00f3n  u sub t + (u elevado m) sub x = 0.  este resultado completa estudios anteriores sobre los rangos de exponentes p &gt; m + 1 y m &lt; p &lt; m + 1.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Comportamiento asintotico de ecuaciones de difusion y conveccion no lineales.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Comportamiento asintotico de ecuaciones de difusion y conveccion no lineales. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Guillermo Reyes Souto <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1999<\/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> Vazquez Suarez Juan  Luis<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Francisco Bernis carro <\/li>\n<li>Alberto Tesei (vocal)<\/li>\n<li>Miguel Escobedo Martinez (vocal)<\/li>\n<li>enrique Zuazua iriondo (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Guillermo Reyes Souto En este tesis se aborda el estudio de comportamiento asint\u00f3tico para tiempos grandes 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 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