{"id":25600,"date":"2022-05-02T12:37:00","date_gmt":"2022-05-02T10:37:00","guid":{"rendered":"https:\/\/cio.umh.es\/?p=25600"},"modified":"2022-05-09T08:53:04","modified_gmt":"2022-05-09T06:53:04","slug":"caballero-r-marin-rubio-p-valero-j-2021-existence-and-characterization-of-attractors-for-a-nonlocal-reaction-diffusion-equation-with-an-energy-functional-journal-of-dynamics-and","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2022\/05\/02\/caballero-r-marin-rubio-p-valero-j-2021-existence-and-characterization-of-attractors-for-a-nonlocal-reaction-diffusion-equation-with-an-energy-functional-journal-of-dynamics-and\/","title":{"rendered":"Caballero, R., Mar\u00edn-Rubio, P., Valero, J. (2022) \u00abExistence and Characterization of Attractors for a Nonlocal Reaction\u2013Diffusion Equation with an Energy Functional\u00bb, Journal of Dynamics and Differential Equations, 34 (1):443\u2013480"},"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) 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 a nonlocal reaction\u2013diffusion equation in which the diffusion depends on the gradient of the solution. Firstly, we prove the existence and uniqueness of regular and strong solutions. Secondly, we obtain the existence of global attractors in both situations under rather weak assumptions by defining a multivalued semiflow (which is a semigroup in the particular situation when uniqueness of the Cauchy problem is satisfied). Thirdly, we characterize the attractor either as the unstable manifold of the set of stationary points or as the stable one when we consider solutions only in the set of bounded complete trajectories.<\/p>","protected":false},"excerpt":{"rendered":"<p>Rub\u00e9n Caballero, Jos\u00e9 Valero (Centro de Investigaci\u00f3n Operativa, Universidad Miguel Hernandez de Elche) and Pedro Mar\u00edn (Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla)<br \/>\nAbstract: In this paper we study a nonlocal reaction\u2013diffusion equation in which the diffusion depends on the gradient of the solution. Firstly, we prove the existence and uniqueness of regular and [&#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\/25600"}],"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=25600"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25600\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=25600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=25600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=25600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}