Asymptotic expansion for layer solutions of a singularly perturbed   reaction-diffusion system
  For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order in $\epsilon$. The formal solution shows that there is an invariant manifold of wave-front-like solutions that attracts other nearby solutions. With an additional assumption on the sign of the wave speed, the wave-front-like solutions converge slowly to stable stationary solutions on that manifold. 
Xiao-Biao Lin (Department of Mathematics, North Carolina State   University, Raleigh, North Carolina)