{"id":92,"date":"2024-10-03T09:58:28","date_gmt":"2024-10-03T12:58:28","guid":{"rendered":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/?p=92"},"modified":"2024-10-11T09:25:59","modified_gmt":"2024-10-11T12:25:59","slug":"tba-2","status":"publish","type":"post","link":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/2024\/10\/tba-2\/","title":{"rendered":"On the reachable space for the heat equation"},"content":{"rendered":"
D\u00cdA \/ HORA:<\/span><\/b> Jueves 17 de octubre 2024 \/ 16:30 – 17:30<\/span><\/div>\n
EXPOSITOR: Sylvain Ervedoza<\/strong>,\u00a0 Institut de Math\u00e9matiques de Bordeaux, Universit\u00e9 de Bordeaux and CNRS<\/div>\n
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RESUMEN<\/span><\/b>: The goal of this talk is to explain how perturbative arguments can be applied to derive a sharp description of the reachable space for heat equations having lower order terms. The main result I will present is the following one. Let us consider an abstract system y’ = Ay + Bu<\/em>, where A is an operator generating a C^0<\/em> semigroup (exp(tA))_{t \u2265\u00a00}<\/em> on a Hilbert space X<\/em>, and B<\/em> is a control operator, for instance a linear operator from an Hilbert space U<\/em> to X<\/em>, and let us assume that this system is null-controllable in X in any positive time. Then, setting R the reachable set of the system (that is all the states that can be achieved by y solution of y’ = Ay + Bu<\/em>, y(0) = 0<\/em>), the restriction of (exp(tA))_{t \u2265\u00a00}<\/em> to R<\/em> forms a C^0<\/em> semigroup on R<\/em>. Accordingly, the system y’ = Ay + Bu<\/em> is exactly controllable on R<\/em>, and one can then perform classical perturbative arguments to handle lower order terms, as I will explain on a few examples. This talk is based on a joint work with K\u00e9vin Le Balc\u2019h (INRIA Paris) and Marius Tucsnak (Bordeaux). If time allows, I will also explain the strategy we develop in a recent work with Adrien Tendani-Soler (Bordeaux) to get a more refined description of the reachable space in the case of a ball controlled from its entire boundary, following the recent approach by Alexander Strohmaier and Alden Waters.<\/span><\/div>\n
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IDIOMA: <\/b>English<\/span><\/p>\n<\/div>\n

LUGAR<\/span><\/b>: Auditorio Ninoslav Bralic, Facultad de Matem\u00e1tica<\/span>, Campus San Joaqu\u00edn, Universidad Cat\u00f3lica de Chile
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DIRECCI\u00d3N:<\/strong> Avda. Vicu\u00f1a Mackenna 4860, Macul, Chile. C\u00f3mo llegar<\/a>.<\/span><\/div>\n
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MODALIDAD:<\/strong> Presencial y transmisi\u00f3n por Microsoft Teams. Para acceder a la transmisi\u00f3n de la charla hacer click aqu\u00ed<\/a>.<\/div>\n","protected":false},"excerpt":{"rendered":"

Sylvain Ervedoza,\u00a0 Institut de Math\u00e9matiques de Bordeaux, Universit\u00e9 de Bordeaux and CNRS<\/p>\n","protected":false},"author":116,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-92","post","type-post","status-publish","format-standard","hentry","category-seminarios"],"_links":{"self":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts\/92","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/comments?post=92"}],"version-history":[{"count":9,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts\/92\/revisions"}],"predecessor-version":[{"id":104,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts\/92\/revisions\/104"}],"wp:attachment":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/media?parent=92"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/categories?post=92"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/tags?post=92"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}