Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 79, pp. 1-14.

Title: Reaction-diffusion systems with 1-homogeneous non-linearity

Author: Matthias Bueger (Justus-Liebig-Univ. Giessen, Germany)
         
Abstract: 
  We describe the dynamics of a system of two reaction-diffusion
  equations with 1-homogeneous non-linearity.
  We show that either an order-preserving property holds and
  can be used in order to determine the limiting behaviour in some
  (invariant) sets or the long time behaviour of all solutions
  can be described by looking at one scalar reaction-diffusion
  equation only.
     
Submitted November 15, 2000. Published September 27, 2002.
Math Subject Classifications: 35K57
Key Words: Reaction-diffusion equations; order-preserving;
           reduction to one equation; oscillation number