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Colliding $p$-branes in the dynamical intersecting brane system

We discuss the dynamics of intersecting $p$-branes with cosmological constants in the higher-dimensional gravity theories. For the delocalized brane case, these solutions describe an asymptotically de Sitter or power-law expanding universe, while for the partially localized intersecting branes, they describe homogeneous and isotropic universes at each position of the overall transverse space. We then apply these time-dependent branes to the study on the collision of two 0-branes and show that the 0$-$8-brane system or the smeared $0-p_I$-brane system can provide an example of colliding branes if they have the same brane charges and only one overall transverse space. Finally, we argue some applications of the solutions in supergravity models.