{"id":481,"date":"2025-07-21T09:57:28","date_gmt":"2025-07-21T08:57:28","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=481"},"modified":"2025-07-21T10:00:29","modified_gmt":"2025-07-21T09:00:29","slug":"el-problema-de-muskat","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/el-problema-de-muskat\/","title":{"rendered":"El problema de Muskat"},"content":{"rendered":"<p>El\u00a0problema de Muskat\u00a0descriu el moviment de la\u00a0interf\u00edcie entre dos fluids immiscibles\u00a0(com aigua i oli) dins d\u2019un\u00a0medi por\u00f3s. Es basa en la\u00a0llei de Darcy (que descriu la velocitat d&#8217;un fluid en un medi por\u00f3s respecte la permeabilitat del medi i les viscositats i pressions del propi fluid) \u00a0i en la\u00a0conservaci\u00f3 de la massa.<\/p>\n<p>Ens centrarem en el cas bidimensional. Aleshores, la interf\u00edcie entre els dos fluids pot ser descrita a priori per la gr\u00e0fica d&#8217;una funci\u00f3, fet que simplifica notablement els c\u00e0lculs.<\/p>\n<p>Conv\u00e9 que l&#8217;estudiant hagi cursat l&#8217;assignatura An\u00e0lisi Real i Funcional o estigui fent-ho, per tal d&#8217;aprofundir en q\u00fcestions relacionades amb l&#8217;exist\u00e8ncia, unicitat i regularitat de les solucions de la equaci\u00f3 en derivades parcials associada al problema.<\/p>\n<p>Un bon punt per comen\u00e7ar pot ser el seg\u00fcent\u00a0<em>survey\u00a0<\/em>sobre el tema.<\/p>\n<p><a href=\"https:\/\/personal.us.es\/fgancedo\/Papers\/SEMAMuskat.pdf\">https:\/\/personal.us.es\/fgancedo\/Papers\/SEMAMuskat.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>El\u00a0problema de Muskat\u00a0descriu el moviment de la\u00a0interf\u00edcie entre dos fluids immiscibles\u00a0(com aigua i oli) dins d\u2019un\u00a0medi por\u00f3s. Es basa en la\u00a0llei de Darcy (que descriu la velocitat d&#8217;un fluid en un medi por\u00f3s respecte la permeabilitat del medi i les viscositats i pressions del propi fluid) \u00a0i en la\u00a0conservaci\u00f3 de la massa. Ens centrarem en [&hellip;]<\/p>\n","protected":false},"author":74,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29,30],"tags":[47],"class_list":["post-481","post","type-post","status-publish","format-standard","hentry","category-analisi-matematica","category-matematica-aplicada","tag-juan-carlos-cantero"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/481","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/74"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=481"}],"version-history":[{"count":4,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/481\/revisions"}],"predecessor-version":[{"id":485,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/481\/revisions\/485"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=481"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=481"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=481"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}