  We study dynamical partially localized brane solutions in higher dimensions.
We give new descriptions of the relevant solutions of dynamical branes which
are localized along both the overall and relative transverse directions. The
starting point is a system of p_r-branes ending on a p_s-brane with a
time-dependent warp factor. This system can be related to Dp_r-Dp_s brane
system in string theory, where one brane is localized at the delocalized other
brane. We then show that these give Friedmann-Lemaitre-Robertson-Walker
cosmological solutions. Our approach leads to a new and manifest description of
the brane configurations near the delocalized branes, and new solutions in the
wave or KK-monopole background in terms of certain partial differential
equations in D dimensions including ten and eleven dimensions.
