  The embedding of a thick de Sitter 3-brane into a five-dimensional bulk is
studied, assuming a scalar field with potential is present in the bulk. A class
of solutions is found in closed form that can represent a thick de Sitter
3-brane interpolating either between two dynamical black holes with a $R \times
S_{4}$ topology or between two Rindler-like spacetimes with a $R_{2}\times
S_{3}$ topology. The gravitational field is localized in a small region near
the center of the 3-brane. The analysis of graviton fluctuations shows that a
zero mode exists and separates itself from a set of continuous modes by a mass
gap. The existence of such a mass gap is shown to be universal. The scalar
perturbations are also studied and shown to be stable.
