  We consider a deformation of the $AdS_5\times S^5$ solution of IIB
supergravity obtained by taking the boundary value of the dilaton to be time
dependent. The time dependence is taken to be slowly varying on the AdS scale
thereby introducing a small parameter $\epsilon$. The boundary dilaton has a
profile which asymptotes to a constant in the far past and future and attains a
minimum value at intermediate times. We construct the sugra solution to first
non-trivial order in $\epsilon$, and find that it is smooth, horizon free, and
asymptotically $AdS_5\times S^5$ in the far future. When the intermediate
values of the dilaton becomes small enough the curvature becomes of order the
string scale and the sugra approximation breaks down. The resulting dynamics is
analysed in the dual SU(N) gauge theory on $S^3$ with a time dependent coupling
constant which varies slowly. When $N \epsilon \ll 1$, we find that a quantum
adiabatic approximation is applicable, and use it to argue that at late times
the geometry becomes smooth $AdS_5\times S^5$ again. When $N \epsilon \gg 1$,
we formulate a classical adiabatic perturbation theory based on coherent states
which arises in the large $N$ limit. For large values of the 'tHooft coupling
this reproduces the supergravity results. For small 'tHooft coupling the
coherent state calculations become involved and we cannot reach a definite
conclusion. We argue that the final state should have a dual description which
is mostly smooth $AdS_5$ space with the possible presence of a small black
hole.
