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We present a class of dynamical solutions for intersecting D4-D8 and D3-D7brane systems in ten-dimensional type IIA and IIB supergravity. We discuss ifthese solutions can be recovered in lower-dimensional effective theories forthe warped compactification of a general p-brane system. It is found that aneffective $p+1$-dimensional description is not possible in general due to theentanglement of the transverse coordinates and the $p+1$-dimensionalcoordinates in the metric components. For the D4-D8 brane system, the dynamicalsolutions reduces to a static warped ${\rm AdS_6}\times {\rm S}^4$ geometry ina certain spacetime region. For the D3-D7 brane system, we find a dynamicalsolution whose metric form is similar to that of a D3-brane solution. The maindifference is the existence of a nontrivial dilaton configuration in the D3-D7solution. Then we discuss cosmology of these solutions. We find that theybehave like a Kasner-type cosmological solution at $\tau\to\infty$, while itreduces to a warped static solution at $\tau\to0$, where $\tau$ is the cosmictime.

Dynamical D4-D8 and D3-D7 branes in supergravity