{"id":410,"date":"2016-06-17T06:46:22","date_gmt":"2016-06-17T06:46:22","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/?p=410"},"modified":"2016-06-17T06:46:22","modified_gmt":"2016-06-17T06:46:22","slug":"generalized-junction-conditions-for-degenerate-parabolic-equations","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/generalized-junction-conditions-for-degenerate-parabolic-equations\/","title":{"rendered":"Generalized junction conditions for degenerate parabolic equations"},"content":{"rendered":"<p><em>Vinh Nguyen\u00a0(Cardiff, UK)<\/em><\/p>\n<p>With C.\u00a0IMBERT, we study degenerate parabolic equations in\u00a0multi-domains\u00a0whose coefficients are discontinuous along interfaces.\u00a0\u00a0We observe that the approach proposed by IMBERT\u00a0and Monneau (2014) for Hamilton-Jacobi equations can be further developed to handle generalized junction conditions (such as the generalized Kirchoff ones) and second order terms. We first prove that generalized junction conditions reduce to flux-limited ones. \u00a0We then use then vertex test function (Imbert, Monneau &#8212; 2014) to prove a comparison principle. \u00a0We\u00a0 then\u00a0determine the vanishing viscosity limit associated with Hamilton-Jacobi equations posed on multi-domains and networks. \u00a0In the two-domain and convex case, the maximal Ishii solution identified by Barles, Briani and Chasseigne (2012) is selected. Finally, we give a short and simple PDE proof for the large deviation result of Boue, Dupuis and Ellis (2000).<\/p>\n<p><a href=\"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/programme\/\">Back to Programme<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vinh Nguyen\u00a0(Cardiff, UK) With C.\u00a0IMBERT, we study degenerate parabolic equations in\u00a0multi-domains\u00a0whose coefficients are discontinuous along interfaces.\u00a0\u00a0We observe that the approach proposed by IMBERT\u00a0and Monneau (2014) for Hamilton-Jacobi equations can be further developed to handle generalized junction conditions (such as the generalized Kirchoff ones) and second order terms. We first prove that generalized junction conditions reduce &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/generalized-junction-conditions-for-degenerate-parabolic-equations\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Generalized junction conditions for degenerate parabolic equations<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-410","post","type-post","status-publish","format-standard","hentry","category-abstracts"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/410","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/comments?post=410"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/410\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/media?parent=410"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/categories?post=410"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/tags?post=410"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}