{"id":11841,"date":"2021-10-26T08:39:47","date_gmt":"2021-10-26T00:39:47","guid":{"rendered":"https:\/\/virtual.math.ntnu.edu.tw\/?p=11841"},"modified":"2021-10-26T08:41:34","modified_gmt":"2021-10-26T00:41:34","slug":"001-43","status":"publish","type":"post","link":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/2021\/10\/26\/001-43\/","title":{"rendered":"[FALL 2021 Nonlinear Analysis Seminar Series] <\/span>\u301012\u67087\u65e5\u3011On a singular limit of a single-well Modica-Mortola functional and its applications, Yoshikazu Giga"},"content":{"rendered":"

Nonlinear Analysis Unit (Daniel Spector)
\nFALL 2021 Nonlinear Analysis Seminar Series<\/p>\n

https:\/\/groups.oist.jp\/nonlinearanalysis\/fall-2021-nonlinear-analysis-seminar-series<\/a><\/span><\/p>\n

Tuesday 7th December 2021, 15:00\u201316:00, online on Zoom or M210<\/span><\/h3>\n

Speaker\uff1a<\/span>Yoshikazu Giga<\/span><\/a>,\u00a0 The University of Tokyo<\/h3>\n

Title: On a singular limit of a single-well Modica-Mortola functional and its applications<\/h3>\n

Abstract:<\/h3>\n

It is important to describe the motion of phase boundaries by macroscopic energy in the process of phase transitions. Typical energy describing the phenomena is the van der Waals energy, which is also called a Modica-Mortola functional with a double-well potential or the Allen-Cahn functional. It turns out that it is also important to consider the Modica-Mortola functional with a single-well potential since it is often used in various settings including the Kobayashi-Warren-Carter energy, which is popular in materials science. It is very fundamental to understand the singular limit of such a type of energies as the thickness parameter of a diffuse interface tends to zero. In the case of double-well potentials, such a problem is well-studied and it is formulated, for example, as the Gamma limit under\u00a0L<\/span>1<\/span><\/span><\/span><\/span>L1<\/span><\/span>\u00a0convergence.<\/p>\n

However, if one considers the Modica-Mortola functional, it turns out that\u00a0L<\/span>1<\/span><\/span><\/span><\/span>L1<\/span><\/span>\u00a0convergence is too rough even in the one-dimensional problem.<\/p>\n

We characterize the Gamma limit of a single-well Modica-Mortola functional under the topology which is finer than\u00a0L<\/span>1<\/span><\/span><\/span><\/span>L1<\/span><\/span>\u00a0topology. In a one-dimensional case, we take the graph convergence. In higher-dimensional cases, it is more involved. As an application, we give an explicit representation of a singular limit of the Kobayashi-Warren-Carter energy. Since the higher-dimensional cases can be reduced to the one-dimensional case by a slicing argument, studying the one-dimensional case is very fundamental. A key idea to study the one-dimensional case is to introduce \u201can unfolding of a function\u201d by changing an independent variable by the arc-length parameter of its graph. This is based on a joint work with Jun Okamoto (The University of Tokyo), Masaaki Uesaka (The University of Tokyo, Arithmer Inc.), and Koya Sakakibara (Okayama University of Science, RIKEN).<\/p>\n

Please click here to register<\/a><\/strong><\/span>
\n*After registering, you will receive a confirmation email containing information about joining the meeting.<\/h5>\n

\u53cb\u5584\u5217\u5370<\/a><\/p>","protected":false},"excerpt":{"rendered":"

Nonlinear Analysis Unit (Daniel Spector) FALL 2021 Nonl […]<\/p>\n","protected":false},"author":18,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1,18,122,124],"tags":[],"_links":{"self":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/11841"}],"collection":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/users\/18"}],"replies":[{"embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/comments?post=11841"}],"version-history":[{"count":3,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/11841\/revisions"}],"predecessor-version":[{"id":11845,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/11841\/revisions\/11845"}],"wp:attachment":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/media?parent=11841"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/categories?post=11841"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/tags?post=11841"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}