Abstract: In this paper, the author considered the singular perturbation of mixed boundaryvalue problem for a class sixth order elliptic equation when the limit equation is degenearatedelliptic equation (elliptic-parabolic) at the partial boundary. Under suitable assumptions, usingthe improving method of multiple scale, the uniformly valid asymptotic expansion of solutioninvolving boundary layer and cover layer of arbitrary order at the whole half-circle region is ob-tained except two corner point at the half-circle region.

Key words: Eiliptic-parabolic, singular perturbation, asymptotic expansion