※このページは北大数学COEで作成しています
第６回諸分野のための数学研究会 (北大数学COE協賛)
Seminar on Mathematics for various disciplines
Program
- 日 時：
- 2006年7月5日(水) 10:30-11:30
- 場 所：
- 東京大学大学院 数理科学研究科056号室
※会場へのアクセスは下記にてご確認下さい。
駒場アクセスマップ
http://www.u-tokyo.ac.jp/campusmap/map02_02_j.html
駒場キャンパス数理科学研究科棟
http://www.u-tokyo.ac.jp/campusmap/cam02_01_27_j.html
- プログラム：
-
- Professor Y. H. Richard Tsai (University of Texas)
- Level Set Methods and Multi-valued solutions
- ABSTRACT:
- We review the level set methods for computing multi-valued solutions to a class of nonlinear first order partial differential equations, including Hamilton-Jacobi equations, quasi-linear hyperbolic equations, and conservative transport equations with multi-valued transport speeds. The multivalued solutions are embedded as the zeros of a set of scalar functions that solve the initial value problems of a time dependent partial differential equation in an augmented space. We discuss the essential ideas behind the techniques, the coupling of these techniques to the projection of the interaction of zero level sets and a collection of applications including the computation of the semiclassical limit for Schr\"{o}dinger equations and the high frequency geometrical optics limits of linear wave equations.
