On Monday, 27 November 2023 at - 12 PM for Beijing, Hong Kong and Perth - 1 PM for Seoul and Tokyo - 3 PM for Canberra, Melbourne and Sydney - 5 PM for Auckland Masashi Misawa (Professor @ Kumamoto University, Japan) is speaking at the Asia-Pacific Analysis and PDE Seminar on Title: Concentration phenomenon for the Sobolev flow Abstract: We shall study the asymptotic behavior at infinite-time of the Sobolev flow. The Sobolev flow describes the gradient flow associated with the Sobolev inequality and is given as a doubly nonlinear parabolic equation. We present the global existence for Cauchy-Dirichlet problem for the Sobolev flow, a boundedness, a positivity and a regularity of the solution. The behavior at infinity-time of the Sobolev flow is studied using the local boundedness of the solution. The local boundedness is the new ingredient obtained for the doubly nonlinear parabolic equation. The concentration phenomenon of volume and energy at infinite-time is shown by the local boundedness. Chair: Yoshikazu Giga (Professor @ University of Tokyo, Japan) The format of the seminar: - The Seminar is held in form of a 45 minutes lecture in a Zoom Webinar. - The talk is followed-up by a 15 minutes Q&A discussion guided by the chair of the talk. - Attendees please say "Hello, I am from University X!" in the Chat upon entering the Webinar. Since the Zoom Webinar does not provide a "list of attendees" to the attendees, please identify yourself in the "Chat" upon entering the Zoom Webinar with a short sentence! To join this Zoom Webinar, you can copy and paste the following link into your internet browser: https://uni-sydney.zoom.us/w/85852446121?tk=1tHe66JhVgzZD8e2TsOgmE7PzYHzlbQ__Sl7tSFpWzk.DQUAAAAT_TRdqRpmYWtld1BFODdDNXJUNkNFUDBlOFJEQWlSdwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA More information and how to attend this talk can be found at the seminar webpage