Abstract
We prove stability of the family of Kasner solutions within the class of polarized
T
2
-symmetric solutions of the vacuum Einstein equations in the contracting time direction with respect to an areal time foliation. All Kasner solutions for which the asymptotic velocity parameter
K
satisfies
|
K
-
1
|
>
2
are non-linearly stable, and all sufficiently small perturbations exhibit asymptotically velocity term dominated (AVTD) behavior and blow-up of the Kretschmann scalar.