State-constrained porous media control systems with application to stabilization

We aim at providing a characterization of the ability to maintain a stochastic coupled system with porous media components in a prescribed set of constraints by using internal controls. This property is proven via a quasi-tangency local-in-time condition in the spirit of Euler approximation schemes. In particular, by employing one of the components of the system as asymptotic supervisor, we give conditions guaranteeing the exponential asymptotic stabilizability of controlled porous media equations.

Automated summary

This paper aims to characterize the ability to maintain a stochastic coupled system with porous media components in a prescribed set of constraints by using internal controls. This property is proven by establishing a quasi-tangency local-in-time condition inspired by Euler approximation schemes. Specifically, by utilizing one of the components of the system as an asymptotic supervisor, conditions for the exponential asymptotic stabilizability of controlled porous media equations are provided.