  This paper concerns the dynamic stability of the steady 3-D wave structure of
a planar normal shock front intersecting perpendicularly to a planar solid wall
for unsteady potential flows. The stability problem can be formulated as a free
boundary problem of a quasi-linear hyperbolic equation of second order in a
dihedral-space domain between the shock front and the solid wall. The key
difficulty is brought by the edge singularity of the space domain, the
intersection curve between the shock front and the solid wall. Different from
the 2-D case, for which the singular part of the boundary is only a point, it
is a curve for the 3-D case in this paper. This difference brings new
difficulties to the mathematical analysis of the stability problem. A modified
partial hodograph transformation is introduced such that the extension
technique developed for the 2-D case can be employed to establish the
well-posed theory for the initial-boundary value problem of the linearized
hyperbolic equation of second order in a dihedral-space domain. Moreover, the
extension technique is improved in this paper such that loss of regularity in
the a priori estimates on the shock front does not occur. Thus the classical
nonlinear iteration scheme can be constructed to prove the existence of the
solution to the stability problem, which shows the dynamic stability of the
steady planar normal shock without applying the Nash-Moser iteration method.
