Validity of the linear marginal stability principle for monotonic fronts of the extended Fisher-Kolmogorov equation

Abstract

The extended Fisher Kolmogorov equation $u_t=u_{xx}-\gamma u_{xxxx}+f(u)$ with arbitrary positive $f(u)$, satisfying $f(0)=f(1)=0$, has monotonic traveling fronts for $\gamma <1/12$. We find a simple lower bound on the speed of the fronts which allows to assess the validity of linear marginal stability.

3 pages, no figures