Im Februar war Herr Paul Carter zu Gast am Lehrstuhl für Analysis und Modellierung und sprach am 19.02.2018 im Lehrstuhlseminar zum Thema "Traveling waves in multiple timescale reaction-diffusion systems".
Photo:
Björn de Rijk, PhD. (l)
Paul Carter, PhD. (r)
Abstract: Reaction diffusion PDEs are prototypical models in the study of pattern forming processes. Within these models, many such patterns can be interpreted as traveling waves, which are profiles with fixed shape which move with constant speed, and manifest as solutions of an associated traveling wave ODE. We discuss methods for constructing traveling waves in systems with timescale separation, in which the dynamics of one or more components is slow relative to the others. We present existence results for traveling pulse solutions in two example applications: vegetation stripe patterns in semiarid regions, described by the Klausmeier equation, and nerve impulse propagation, described by the FitzHugh--Nagumo equation. The existence proofs rely on the slow/fast nature of the traveling wave equations and the techniques of geometric singular perturbation theory and blow-up desingularization.