Instability of singularly perturbed Neumann layer solutions in reaction-diffusion systems

Instability of mono-Neumann layer solutions to reaction-diffusion systems is proved by using the SLEP method. Mono-Neumann layers are singularly perturbed solutions of boundary layer type which are close to thestable constant state except in a neighborhood of a boundary point and satisfy the Neumann boundary conditions. We also show the dimension of the associated unstable manifold and the asymptotic behavior of the unstable eigenvalue when one of the diffusion coefficients tends to zero.