  In this paper, we discuss the time-dependent brane solutions in
higher-dimensional supergravity theories. We particularly focus on the
dynamical extensions of the intersecting brane solutions involving three
branes. We also show that in the near-horizon limits, where the time dependence
is negligible, these branes describe warped anti-de Sitter spacetimes as in the
corresponding static solutions. We finally examine the lower-dimensional
cosmological dynamics obtained after compactifications of the
higher-dimensional solutions and show the solutions we have found give the
four-dimensional universe with power-law expansion.
