Seminar on Mathematics for various disciplines

Seminar information archive ~07/20Next seminarFuture seminars 07/21~

Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2006/07/05

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
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 omputation of the semiclassical limit for Schr\\"{o}dinger quations and the high frequency geometrical optics limits of linear wave equations.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html