Existence of additional unstable equilibria and travelling waves for some monostable systems
by
Elaine Crooks
Oxford University

We prove the existence of additional unstable equilibria E^± for a class of "monostable" reaction-diffusion systems

ut = A uxx + f(u),    u(x, t) ∈ RN,

having known equilibria S < T with S "stable" and T "unstable" such that the derivative df[T] has an even number of unstable eigenvalues. The proofs use degree theory and positive-operator theory. Systems in the class considered are known to admit monotone increasing travelling-front solutions w(x-ct) connecting ordered stable and unstable equilibria for all c greater than or equal to a positive critical value and the existence of E^± > S yields two one-parameter families of travelling fronts connecting S to E^± in addition to the family connecting S to T.

Date received: June 19, 2007

Copyright © 2007 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 # cavg-15.