  The aim of the present paper is to provide necessary and sufficient
conditions to maintain a stochastic coupled system, with porous media
components and gradient-type noise in a prescribed set of constraints by using
internal controls. This work is a continuation of the results in [10], as we
consider the case of divergence type noise perturbation. On the other hand, it
provides a different framework in which the quasi-tangency condition can be
obtained with optimal speed. In comparison with the aforementioned result, here
we transform the stochastic system into a random deterministic one, via the
rescaling approach, then we study the viability of random sets. As an
application, conditions for the stabilization of the stochastic porous media
equations are obtained.
