  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.

Analysis of PDEs