Speaker: Blake Barker (Brigham Young University)
Title: Stability of sharp fronts: computer assisted methods of proof
Abstract: Using a combination of analytic and computer assisted methods of proof, we prove stability of traveling front solutions to the KdV-Burgers equation. The methods apply much more generally. In this talk we focus on the rigorous computations involved in the computer assisted methods of proof. We use a Newton-Kantorovich argument and the parametrization method to rigorously enclose the traveling wave profile and the Riccati equation. We use analytic interpolation of the ODE series solution coefficients in order to establish the result for values of the dispersion parameter ranging over an interval.
