Friday, October 9 at 3:30pm, Virtual Room (Zoom Meeting ID: 754 716 1091)

"Asymptotic analysis and numerical computations of some boundary value problems"
Dr. Gung-Min Gie, University of Louisville

Abstract:

In the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. Boundary value problems arise in physics and other fields, e.g., Black--Scholes equation in financial math, Navier--Stokes equations in fluid mechanics, and Keller--Segel equations in math biology. In this talk, we consider a simple 1D (or 2D) boundary value problem, which consists of a convection--(reaction)--diffusion equation, supplemented with appropriate boundary conditions. Concerning this model problem, we analyze the asymptotic behavior of solutions at the vanishing diffusivity, and discuss the related numerical computations. Some recent progress in this research direction will be introduced as well.