  We present time-dependent solutions in the higher-dimensional gravity which
are related to supergravity in the particular cases. Here, we consider p-branes
with a cosmological constant and the intersections of two and more branes. The
dynamical description of p-branes can be naturally obtained as the extension of
static solutions. In the presence of a cosmological constant, we find
accelerating solutions if the dilaton is not dynamical. In the case of
intersecting branes, the field equations normally indicate that time-dependent
solutions in supergravity can be found if only one harmonic function in the
metric depends on time. However, if the special relation between dilaton
couplings to antisymmetric tensor field strengths is satisfied, one can find a
new class of solutions where all harmonic functions depend on time. We then
apply our new solutions to study cosmology, with and without performing
compactifications.
