Edge bifurcations for singularly perturbed reaction-diffusion equations
by
Arjen Doelman
University of Amsterdam
Coauthors: David Iron (Amsterdam), Yasumasa Nishiura (Hokkaido)

We consider the stability of front solutions to a certain class of bi-stable equations. A leading order analysis indicates that these fronts are destabilized by the essential spectrum of the associated linear operator. However, a more careful analysis shows that there may, or may not, appear (discrete) eigenvalues from the essential spectrum that cause the destabilization. In this talk we will use geometric singular perturbation theory and the Evans function approach to establish a relation between the (geometric) character of the front solution and the occurrence of edge bifurcations.

Date received: June 6, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calo-77.