Colloquium
4:00 p.m., Monday
(February 9th)
Math Bldg. Room 203
Adam Oberman
University of Texas at Austin
Building solutions to nonlinear elliptic and parabolic
partial differential equations
Nonlinear elliptic and parabolic partial differential
equations (PDEs) appear in problems from science, engineering,
atmospheric/ocean studies, image processing, and mathematical finance.
The theory of viscosity solutions has been enormously successful
in addressing the problems of existence, uniqueness,
and stability for a wide class of such equations.
A problem which has not been addressed with as much success
is the construction of solutions. In some cases,
exact solutions formulas exist, but for the most part,
solutions must be found numerically.
In the spirit of the classical 1928 paper of Courant,
Freidrichs, and Lewy which used the finite difference method
to construct solutions of linear PDEs, we construct solutions to
nonlinear degenerate elliptic and parabolic PDEs.
We will present example schemes and computational results, for:
valuation in math finance, motion by mean curvature,
and the infinity Laplacian.
Refreshments will be served at 3:45 p.m. in the Faculty
Lounge, Math
Annex (Room 1115).
