  We present a class of dynamical solutions for intersecting D4-D8 and D3-D7
brane systems in ten-dimensional type IIA and IIB supergravity. We discuss if
these solutions can be recovered in lower-dimensional effective theories for
the warped compactification of a general p-brane system. It is found that an
effective $p+1$-dimensional description is not possible in general due to the
entanglement of the transverse coordinates and the $p+1$-dimensional
coordinates in the metric components. For the D4-D8 brane system, the dynamical
solutions reduces to a static warped ${\rm AdS_6}\times {\rm S}^4$ geometry in
a certain spacetime region. For the D3-D7 brane system, we find a dynamical
solution whose metric form is similar to that of a D3-brane solution. The main
difference is the existence of a nontrivial dilaton configuration in the D3-D7
solution. Then we discuss cosmology of these solutions. We find that they
behave like a Kasner-type cosmological solution at $\tau\to\infty$, while it
reduces to a warped static solution at $\tau\to0$, where $\tau$ is the cosmic
time.
