Inaugural Lectures by Fellows/Associates

Conservation Laws with A Flux Function Discontinuous in the Space Variable

The speaker will discuss conservation laws with a flux function F(x, u) discontinuous in the space variable x arises in several models in physics and engineering and in particular, in modeling of two phase flow in a heterogeneous porous medium, in the modeling of the ideal Clarifier-Thickner unit and traffic flows. In this talk the existence, interface entropy condition, uniqueness and the explicit formula for the solution when F(x, u) is convex in u will be discussed. Approximation of the solution by Godunov type numerical schemes and their convergence analysis with applications to oil reservoir simulations will be presented.