Periodic motions in reaction-diffusion systems
by
Matthias Bueger, University of Giessen, Germany
JWB 208, 3:20pm, Friday May 25, 1997
Abstract
Solutions of one autonomous reaction-diffusion equation on
an interval Omega=(0,1) have been examined by many authors.
In the case of Dirichlet boundary conditions every solution
tends to a fixed point of the reaction-diffusion equation.
We ask if we can get more complicated limiting behaviour if
we look at systems of two autonomous reaction-diffusion
equations on the interval Omega. Given some vectorfield f,
we show that the system
X' = \lambda \Delta X + f(X), X=X(t)=( u(t), v(t) ),
with Dirichlet boundary conditions on Omega has periodic
solutions for some \lambda>0. We determine all fixed points
and all periodic orbits and examine their stability
properties.
Request for preprints and reprints bueger@math.usu.edu
This source can be found at http://www.math.utah.edu/research/