Type: Seminar

Distribution: World

Expiry: 5 Dec 2023

CalTitle1: PDE Seminar -- Talk 1 -- Matano -- Front propagation through a two-dimensional cylinder with saw-toothed boundaries

Auth: hannahb@w1d4n6z2.staff.sydney.edu.au (hbry8683) in SMS-SAML

PDE Seminar: 11:00am Tuesday 5th December Quad S225 Talk 1. at 11 am Speaker: Hiroshi Matano (Professor @ Meiji University, Japan) Title: Front propagation through a two-dimensional cylinder with saw-toothed boundaries. Abstract: In this talk, I will discuss a curvature-dependent motion of plane curves in a two-dimensional infinite cylinder with spatially undulating boundaries. The two ends of the curve slide freely along the boundary of the domain while keeping the constant contact angle of $\pi/2$. The question is whether the curve continues to travel to infinity (propagation) or remains in a bounded area (blocking). The same problem was studied in my earlier work under the assumption that the maximum opening angle and closing angle of the boundaries are less than $\pi/4$ (2006 and 2013, joint work with K.-I. Nakamura and B. Lou). Under this condition, one can show that no singularity develops and the solution remains classical. If the opening and closing angles are larger than $\pi/4$, the middle part of the curve may bump into the boundary of the domain, thereby creating singularities. In this talk, I will discuss the long-time behavior of curves that propagates while creating singularities. Among other things we show that if the bumps are arrayed more densely on the boundary, then the speed of propagation increases. In other words, denser obstacles can facilitate propagation, which may sound somewhat paradoxical. This is joint work with Ryunosuke Mori.

Calendar (ICS file) download, for import into your favourite calendar application

UNCLUTTER for printing

AUTHENTICATE to mark the scnews item as read