Braneworld cosmology for a domain wall embedded in the charged (Anti)-de
Sitter-Schwarzschildblack hole of the five--dimensional
Einstein-Gauss-Bonnet-Maxwell theory is considered. The effective Friedmann
equation for the brane is derived by introducing the necessary surface
counterterms required for a well-defined variational principlein the
Gauss--Bonnet theory and for the finiteness of the bulk space. The asymptotic
dynamics of the brane cosmology is determined and it is found that solutions
with vanishingly small spatial volume are unphysical. The finiteness of the
bulk action is related to the vanishing of the effective cosmological constant
on the brane. An analogy between the Friedmann equation and a generalized
Cardy--Verlinde formula is drawn.Comment: LaTex file 28 pages, typos corrected, one reference is adde