Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system

For a singularly perturbed n-dimensional system of reaction-diffusion equations, assuming that the Oth order solutions possess boundary and internal layers and are stable in each regular and singular region, we construct matched asymptotic expansions for formal solutions in all the regular, boundary, internal and initial layers to any desired order in E. The formal solution shows that there is an invariant manifold of wave-front-like solutions that attracts other nearby solutions. We also give conditions for the wave-front-like solutions to converge slowly to stationary solutions on that manifold.