V. Rottsch\"afer, C. E. Wayne
Existence and stability of traveling fronts in the extended 
Fisher-Kolmogorov equation
(290K, Postscript)

ABSTRACT.  We study traveling wave solutions to a general fourth-order differential 
equation that is a singular perturbation of the Fisher-Kolmogorov 
equation. We apply the geometric method for singularly perturbed 
systems to show that for every positive wavespeed there exists a 
traveling wave. We also find that there exists a critical wave 
speed $c^*$ which divides these solutoins into monotonic ($c\ge c^*$) 
and oscillatory ($c < c^*$) solutions. We show that the monotonic 
fronts are locally stable under perturbations in appropriate weighted 
Sobolev spaces by using various energy functionals.