Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts

 Speaker: Jing An (Duke University)

We will discuss the algebraic structure of a large class of reaction-diffusion equations and use it to study the long-time behavior of the solutions and their convergence to traveling waves in the pulled and pushed regimes, as well as at the pushmi-pullyu boundary. A new quantity named as the shape defect function is introduced to measure the difference between the profiles of the solution and the traveling waves. In particular, the positivity of the shape defect function, combined with a new weighted Hopf-Cole transform and a relative entropy approach, plays a key role in the stability arguments. The shape defect function also gives a new connection between reaction-diffusion equations and reaction conservation laws at the pulled-pushed transition. This is joint work with Chris Henderson and Lenya Ryzhik. 

Time: November 18, 2022 2:30pm-3:30pm
Location: LeConte 205
Host: Siming He