数値解析セミナー

過去の記録 ~03/28次回の予定今後の予定 03/29~

開催情報 火曜日 16:30~18:00 数理科学研究科棟(駒場) 002号室
担当者 齊藤宣一、柏原崇人
セミナーURL https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/

2014年05月12日(月)

16:30-18:00   数理科学研究科棟(駒場) 002号室
Chien-Hong Cho 氏 (National Chung Cheng University)
On the finite difference approximation for blow-up solutions of the nonlinear wave equation (JAPANESE)
[ 講演概要 ]
We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\\alpha}$ $(\\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.
[ 参考URL ]
http://www.infsup.jp/utnas/