  We obtain explicit time dependent brane solutions in M-theory as well as in string theory by solving the reduced equations of motion (which follow from 11-d supergravity) for a class of brane solutions in curved backgrounds. The behaviour of our solutions in both asymptotic and near-horizon limits are studied. It is shown that our time dependent solutions serve as explicit examples of branes in singular, cosmological backgrounds. In some special cases the asymptotic and the boundary AdS solutions can be identified as Milne X R^n spacetime. 
Brane Solutions in Time Dependent Backgrounds in D = 11 Supergravity and   in Type II String Theories