EVENT DETAILS AND ABSTRACT

Title: The Uniqueness ane Existence Results on Viscosity Solutions of the Hele-Shaw and the Stefan Problem
Speaker: Christina Inwon Kim
Speaker Info: University of Texas at Austin
Brief Description:
Special Note:
Abstract:

In this talk we introduce a notion of viscosity solutions for the one phase Hele-Shaw and Stefan problems to describe the behavior of solutions for global time and past singularities. These problems are examples of nongeometric and nonlocal free boundary problems, derived from fluid mechanics and phase transitions. Using maximal principle-type arguments, we show that the viscosity solutions of the porous medium equation uniformly converges to those of the Hele-Shaw problem. We then prove that there is a unique viscosity solution of the Hele-Shaw problem for the given initial data.(Parallel results hold for the Stefan problem.) Finally we briefly remark that our method can be extended to more general cases with nonlinear convex operators.