{"id":1488,"date":"2025-11-11T22:38:23","date_gmt":"2025-11-12T06:38:23","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1488"},"modified":"2025-11-11T22:41:40","modified_gmt":"2025-11-12T06:41:40","slug":"global-behavior-of-multispeed-klein-gordon-system","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/11\/11\/global-behavior-of-multispeed-klein-gordon-system\/","title":{"rendered":"Global Behavior of Multispeed Klein&#8211;Gordon System"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <b>November 18th<\/b>, will be at <strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>Xilu Zhu<\/p>\n<p><strong>Abstract: <\/strong>We explore the long-time behavior of multispeed Klein&#8211;Gordon systems in space dimension two. In terms of Klein&#8211;Gordon systems, the space dimension two is somehow considered as a critical threshold with possible transition from stability to instability. To illustrate this, we first prove a global well-posedness result when Klein&#8211;Gordon systems satisfy Ionescu&#8211;Pausader non-degeneracy conditions and the nonlinearity is assumed to be semilinear. Second, on the other hand, we construct a specific Klein&#8211;Gordon system such that one of the nondegeneracy conditions\u00a0is violated and its solution has an infinite time blowup, which implies a type of ill-posedness.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, November 18th, will be at 3:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Xilu Zhu Abstract: We explore the long-time behavior of multispeed Klein&#8211;Gordon systems in space dimension two. In terms of Klein&#8211;Gordon systems, the space dimension two is somehow considered as a critical threshold with possible transition from stability to instability. To illustrate this, we [&hellip;]<\/p>\n","protected":false},"author":116,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25],"tags":[],"class_list":["post-1488","post","type-post","status-publish","format-standard","hentry","category-fall-2025"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1488","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1488"}],"version-history":[{"count":2,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1488\/revisions"}],"predecessor-version":[{"id":1492,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1488\/revisions\/1492"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1488"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1488"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1488"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}