On conditions for the stability of a two component mixed quasimonotone reaction diffusion equation

A spatially heterogeneous two component mixed quasimonotone system of reaction diffusion equations is considered. The kinetic functions exhibit mixed quasimonotonicity and are, in general, non-autonomous, while the boundary conditions are given by one of three possibilities: homogeneous Dirichlet, homogeneous Neumann, or Neumann with a constant inhomogeneity. Some conditions which yield the stability of such equations are deduced via comparison theorems and subsequently used to investigate the stability of a simple example system. © 2001 Academic Press.