{"id":25603,"date":"2021-10-21T13:00:26","date_gmt":"2021-10-21T11:00:26","guid":{"rendered":"https:\/\/cio.umh.es\/?p=25603"},"modified":"2022-01-21T13:01:56","modified_gmt":"2022-01-21T12:01:56","slug":"caballero-r-carvalho-a-n-marin-rubio-p-valero-j-2021-about-the-structure-of-attractors-for-a-nonlocal-chafee-infante-problem-mathematics-9-41-36-353-2","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2021\/10\/21\/caballero-r-carvalho-a-n-marin-rubio-p-valero-j-2021-about-the-structure-of-attractors-for-a-nonlocal-chafee-infante-problem-mathematics-9-41-36-353-2\/","title":{"rendered":"Caballero, R., Carvalho, A.N., Mar\u00edn-Rubio, P., Valero, J. (2021) \u00abAbout the structure of attractors for a nonlocal chafee-infante problem\u00bb, Mathematics, 9 (4):1\u201336, 353"},"content":{"rendered":"<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Rub\u00e9n Caballero, Jos\u00e9 Valero (Centro de Investigaci\u00f3n Operativa, Universidad Miguel Hernandez de Elche), Alexandre N. Carvalho (Instituto de Ci\u00eancias Matem\u00e1ticas e de Computa\u00e7ao, Universidade de S\u00e3o Paulo) and Pedro Mar\u00edn (Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla)<\/strong><\/p>\n<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Abstract:<\/strong> In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem. First, we analyse the existence and properties of stationary points, showing that the problem undergoes the same cascade of bifurcations as in the Chafee-Infante equation. Second, we study the stability of the fixed points and establish that the semiflow is a dynamic gradient. We prove that the attractor consists of the stationary points and their heteroclinic connections and analyse some of the possible connections.<\/p>","protected":false},"excerpt":{"rendered":"<p>Rub\u00e9n Caballero, Jos\u00e9 Valero (Centro de Investigaci\u00f3n Operativa, Universidad Miguel Hernandez de Elche), Alexandre N. Carvalho (Instituto de Ci\u00eancias Matem\u00e1ticas e de Computa\u00e7ao, Universidade de S\u00e3o Paulo) and Pedro Mar\u00edn (Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla)<br \/>\nAbstract: In this paper, we study the structure of the global attractor for the multivalued semiflow generated [&#8230;]<\/p>","protected":false},"author":5675,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[369888],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25603"}],"collection":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/users\/5675"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=25603"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25603\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=25603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=25603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=25603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}