  The dynamics of interacting bosons in one dimension following the sudden
switching on of a weak disordered potential is investigated. On time scales
before quasiparticles scatter (prethermalized regime), the dephasing from
random elastic forward scattering causes all correlations to decay
exponentially fast, but the system remains far from thermal equilibrium. For
longer times, the combined effect of disorder and interactions gives rise to
inelastic scattering and to thermalization. A novel quantum kinetic equation
accounting for both disorder and interactions is employed to study the
dynamics. Thermalization turns out to be most effective close to the
superfluid-Bose glass critical point where nonlinearities become more and more
important. The numerically obtained thermalization times are found to agree
well with analytic estimates.
