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/