  We study global existence problems and asymptotic behavior of
higher-dimensional inhomogeneous spacetimes with a compact Cauchy surface in
the Einstein-Maxwell-dilaton (EMD) system. Spacelike $T^{D-2}$-symmetry is
assumed, where $D\geq 4$ is spacetime dimension. The system of the evolution
equations of the EMD equations in the areal time coordinate is reduced to a
wave map system, and a global existence theorem for the system is shown. As a
corollary of this theorem, a global existence theorem in the constant mean
curvature time coordinate is obtained. Finally, for vacuum Einstein gravity in
arbitrary dimension, we show existence theorems of asymptotically
velocity-terms dominated singularities in the both cases which free functions
are analytic and smooth.
