  String-inspired cosmologies, whereby a non-singular curvature bounce is
induced by a general-covariant, $T$-duality-invariant, non-local dilaton
potential, are used to study numerically how inhomogeneities evolve and to
compare the outcome with analytic expressions obtained through different
matching conditions across the bounce. Good agreement is found if continuity
across the bounce is assumed to hold for $\cal{R}$, the curvature perturbation
on comoving hypersurfaces, rather than for the Bardeen potential.
