We consider the initial-boundary value problem for a single
semilinear parabolic equation with small diffusion rate under the
homogeneous Neumann boundary condition. Bates, Lu and Zeng proved the
existence of a normally hyperbolic invariant manifold for this type of
problem. The manifold consists of functions with a spike on the
boundary, by which we mean that the function attains its maximum at
exactly one point on the boundary and decays exponentially outside a
small neighborhood of the maximum point. Moreover, they proved that the
principal part of the movement of the maximum point of the solution is
the gradient flow of the mean curvature function of the boundary. We are
interested in the movement of the spike near the critical point of the
mean curvature function. In this talk we establish the algorithm to
derive the asymptotic expansion of the equation of motion for the peak
point.