  We consider a class of domain-wall black hole solutions in the dilaton
gravity with a Liouville-type dilaton potential. Using the surface counterterm
approach we calculate the stress-energy tensor of quantum field theory (QFT)
corresponding to the domain-wall black hole in the domain-wall/QFT
correspondence. A brane universe is investigated in the domain-wall black hole
background. When the tension term of the brane is equal to the surface
counterterm, we find that the equation of motion of the brane can be mapped to
the standard form of FRW equations, but with a varying gravitational constant
on the brane. A Cardy-Verlinde-like formula is found, which relates the entropy
density of the QFT to its energy density. At the moment when the brane crosses
the black hole horizon of the background, the Cardy-Verlinde-like formula
coincides with the Friedmann equation of the brane universe, and the Hubble
entropy bound is saturated by the entropy of domain-wall black holes.
