  The recent discovery of an explicit dynamical description of p-branes makes
it possible to investigate the existence of intersection of such objects. We
generalize the solutions depending on the overall transverse space coordinates
and time to those which depend also on the relative transverse space and
satisfy new intersection rules. We give classification of these dynamical
intersecting brane solutions involving two branes, and discuss the application
of these solutions to cosmology and show that these give
Friedmann-Lemaitre-Robertson-Walker cosmological solutions. Finally, we
construct the brane world models, using the (cut-)copy-paste method after
compactifying the trivial spatial dimensions. We then find that interesting
brane world models can be obtained from codimension-one branes and several
static branes with higher codimensions. We also classify the behaviors of the
brane world near the future/past singularity.
