Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3

Numerische Analyse äquivarianter Evolutionsgleichungen

11-079 Jens Rottmann-Matthes.
Stability and Freezing of Waves in Nonlinear Hyperbolic-Parabolic Systems

In this note we consider the application of the freezing method to the approximation of traveling waves in hyperbolic-parabolic systems such as the Hodgkin-Huxley model and the FitzHugh-Nagumo equation. The tuple consisting of the profile and the speed of a traveling wave is a stationary solution for the method and we prove its asymptotic stability with optimal rates. Therefore, the method is suitable for the approximation of traveling waves by time integration. Numerical experiments for the FitzHugh-Nagumo equations confirm our results.