## Tuesday Seminar of Analysis

Date, time & place Tuesday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

### 2022/05/31

16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
OKABE Shinya (Tohoku University)
Convergence of Sobolev gradient trajectories to elastica (Japanese)
[ Abstract ]
In this talk we consider a higher order Sobolev gradient flow for the modified elastic energy defined on closed space curves. The $L^2$-gradient flow for the modified elastic energy has been well studied, and standard results are solvability of the flow for smooth initial curve and subconvergence of solutions to elastica. Moreover, stronger convergence results, so called full limit convergence, are generally up to reparametrisation and sometimes translation. In this talk, we consider $H^2$-gradient flow for the modified elastic energy and prove (i) the solvability of the flow for initial curve in the energy class, (ii) full limit convergence to elastica by way of a Lojasiewicz—Simon gradient inequality. This talk is based on a joint work with Philip Schrader (Murdoch University).
[ Reference URL ]
https://forms.gle/wkCbqdmNuz9zr3vA8