Reaction-diffusion systems with 1-homogeneous non-linearity

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

Keywords

• Reaction-diffusion equations
• order-preserving
• reduction to one equation
• oscillation number