Applied Mathematics Colloquium with Chris Henderson: Quantitative Stability of Traveling Waves

Speaker: Chris Henderson, University of Arizona

Title: Quantitative Stability of Traveling Waves

Abstract:

In their original paper, Kolmogorov, Petrovsky, and Piskunov demonstrated stability of the minimal speed traveling wave with an ingenious compactness argument based on, roughly, the decreasing steepness of the profile.  This proof is extremely flexible, yet entirely not quantitative.  On the other hand, more modern PDE proofs of this fact for general reaction-diffusion equations are highly tailored to the particular equation, fairly complicated, and often not sharp in the rate of convergence.  In this talk, which will be elementary and self-contained, I will introduce a natural quantity, the shape defect function, that allows a simple approach to quantifying convergence to the traveling wave for a large class of reaction-diffusion equations.  This is a joint work with Jing An and Lenya Ryzhik.

 

Applied Mathematics Colloquia