{"id":497,"date":"2018-09-07T15:16:46","date_gmt":"2018-09-07T15:16:46","guid":{"rendered":"http:\/\/pages.charlotte.edu\/colloquium\/?p=497"},"modified":"2018-09-07T15:16:46","modified_gmt":"2018-09-07T15:16:46","slug":"wednesday-sept-12-400pm-500-pm-conference-room","status":"publish","type":"post","link":"https:\/\/pages.charlotte.edu\/colloquium\/blog\/2018\/09\/07\/wednesday-sept-12-400pm-500-pm-conference-room\/","title":{"rendered":"Wednesday, Sept 12, 4:00PM-5:00 PM, Conference room"},"content":{"rendered":"<table>\n<tbody>\n<tr style=\"height: 24px\">\n<td style=\"height: 24px\">Professor: Prof. <a href=\"https:\/\/www.uaf.edu\/dms\/avdonin\/\">Sergei. Avdonin<\/a>, Univ. of Alaska, Fairbanks<\/td>\n<\/tr>\n<tr style=\"height: 24px\">\n<td style=\"height: 24px\">Title:\u00a0<span style=\"font-size: inherit\">Control and Inverse Problems for Differential\u00a0<\/span><span style=\"font-size: inherit\">Equations on Graphs<\/span><\/td>\n<\/tr>\n<tr style=\"height: 144px\">\n<td style=\"height: 144px\">Abstract:\u00a0<span style=\"font-size: inherit\">Quantum graphs are metric graphs with differential equations defined on the\u00a0<\/span><span style=\"font-size: inherit\">edges. Recent interest in control and inverse problems for quantum graphs\u00a0<\/span><span style=\"font-size: inherit\">is motivated by applications to important problems of classical and quantum\u00a0<\/span><span style=\"font-size: inherit\">physics, chemistry, biology, and engineering.<\/span>In this talk we describe some new controllability and identifiability results<br \/>\nfor partial differential equations on compact graphs. In particular, we consider\u00a0graph-like networks of inhomogeneous strings with masses attached at the interior vertices. We show that the wave transmitted through a mass is more\u00a0regular than the incoming wave. Therefore, the regularity of the solution to\u00a0the initial boundary value problem on an edge depends on the combinatorial\u00a0distance of this edge from the source, that makes control and inverse problems\u00a0for such systems more difficult.<\/p>\n<p>We prove the exact controllability of the systems with the optimal number\u00a0of controls and propose an algorithm recovering the unknown densities of the\u00a0strings, lengths of the edges, attached masses, and the topology of the graph.<\/p>\n<p>The proofs are based on the boundary control and leaf peeling methods de-<br \/>\nveloped in our previous papers. The boundary control method is a powerful\u00a0method in inverse theory which uses deep connections between controllability\u00a0and identifiability of distributed parameter systems and lends itself to straight-forward algorithmic implementations.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Professor: Prof. Sergei. Avdonin, Univ. of Alaska, Fairbanks Title:\u00a0Control and Inverse Problems for Differential\u00a0Equations on Graphs Abstract:\u00a0Quantum graphs are metric graphs with differential equations defined on the\u00a0edges. Recent interest in control and inverse problems for quantum graphs\u00a0is motivated by applications to important problems of classical and quantum\u00a0physics, chemistry, biology, and engineering.In this talk we describe [&hellip;]<\/p>\n","protected":false},"author":333,"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":[1],"tags":[],"class_list":["post-497","post","type-post","status-publish","format-standard","hentry","category-spring-2022"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3kCtT-81","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/497","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\/333"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/comments?post=497"}],"version-history":[{"count":1,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/497\/revisions"}],"predecessor-version":[{"id":498,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/497\/revisions\/498"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/media?parent=497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/categories?post=497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/tags?post=497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}