Analysis, Dynamics, and Applications seminar: Ryan Patterson.

Convergence Rates to Traveling Waves for Reaction Diffusion Equations

The KPP equation is a reaction diffusion equation which exhibits a special solution called traveling waves. Under certain assumptions on the reaction term, solutions to the KPP equation converge in shape to a traveling wave. I will present results on the rates at which solutions converge to the traveling wave for the Hadeler-Rothe nonlinearities. These results are proven with energy methods, the main tool being a weighted Nash inequality. This approach is different from the often used comparison principle approach, and generalizes more easily to reaction diffusion systems.