PDE Seminar Representation Formula of Solutions for Parabolic Equations via Optimal Control Problem

2008-05-26 16:30 - 2008-05-26 17:30
Faculty of Science Building #8 Room 309
Kouta Kasai (Hokkaido Univ.)
In this lecture, we give a representation formula of a solutionfor an initial value problem. Such representation is derived bya parametrized value function of an appropriate discrete deterministictwo-person game. Roughly speaking, the value function is constructedvia an initial value and a "minmax" operator, and the limit of valuefunction conforms with a viscosity solution of the correspondingproblem. The game which we consider is based on the game introducedin the recent work of Kohn and Serfaty. We extend their results tomore general cases by adding the concept of interest rate.