{"id":711,"date":"2022-09-12T19:08:25","date_gmt":"2022-09-12T19:08:25","guid":{"rendered":"https:\/\/pages.charlotte.edu\/colloquium\/?p=711"},"modified":"2022-09-15T17:40:45","modified_gmt":"2022-09-15T17:40:45","slug":"friday-september-23-2022-1100-1200","status":"publish","type":"post","link":"https:\/\/pages.charlotte.edu\/colloquium\/blog\/2022\/09\/12\/friday-september-23-2022-1100-1200\/","title":{"rendered":"Friday, September 23, 2022, 02:30-03:30"},"content":{"rendered":"\n<p><strong>Speaker:<\/strong>&nbsp;Khai Nguyen,  Professor of Mathematics, NC State University<\/p>\n\n\n\n<p><strong>Title<\/strong>: Shocks interaction for the Burgers-Hilbert Equation<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: In 2009 J. Biello and J. Hunter derived a balance law modeling nonlinear waves with constant frequency, obtained from Burgers&#8217; equation by adding the Hilbert transform as a source term.\u00a0 For general L^2(R) initial data, the global existence of entropy weak \u00a0solutions was proved by Bressan and Nguyen in 2014, together with a partial uniqueness result. Recently, unique piecewise continuous solutions with a single shock and the shock formation have been recently studied. This talk will describe a further type of local generic singularities for solutions, namely, points where two shocks interact.\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker:&nbsp;Khai Nguyen, Professor of Mathematics, NC State University Title: Shocks interaction for the Burgers-Hilbert Equation Abstract: In 2009 J. Biello and J. Hunter derived a balance law modeling nonlinear waves with constant frequency, obtained from Burgers&#8217; equation by adding the Hilbert transform as a source term.\u00a0 For general L^2(R) initial data, the global existence of [&hellip;]<\/p>\n","protected":false},"author":2756,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[13],"tags":[],"class_list":["post-711","post","type-post","status-publish","format-standard","hentry","category-fall-2022"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3kCtT-bt","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/711","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/users\/2756"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/comments?post=711"}],"version-history":[{"count":4,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/711\/revisions"}],"predecessor-version":[{"id":723,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/711\/revisions\/723"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/media?parent=711"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/categories?post=711"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/tags?post=711"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}