  We present dynamical intersecting brane solutions in higher-dimensional
gravitational theory coupled to dilaton and several forms. Assuming the forms
of metric, form fields, and dilaton field, we give a complete classification of
dynamical intersecting brane solutions with/without M-waves and Kaluza-Klein
monopoles in eleven-dimensional supergravity. We apply these solutions to
cosmology and black holes. It is shown that these give FRW cosmological
solutions and in some cases Lorentz invariance is broken in our world. If we
regard the bulk space as our universe, we may interpret them as black holes in
the expanding universe. We also discuss lower-dimensional effective theories
and point out naive effective theories may give us some solutions which are
inconsistent with the higher-dimensional Einstein equations.
