  We derive exact solutions of the Einstein equations in the context of the
Randall-Sundrum model with matter on the brane and in the bulk. We present two
models in which the brane moves within a time-dependent bulk. We study the
cosmological evolution on the brane. Our solutions display novel behaviour,
such as an expansion driven only by the bulk matter and the appearance of a
``mirage'' dust component on the brane.
