The 6th : Seminar on Mathematics for various disciplines

Place :: Graduate School of Mathematical Sciences the University of Tokyo, Room #056

Programme :

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.

6th Seminar on Mathematics for various disciplines