Asymptotic issue for porous media systems with linear multiplicative gradient-type noise via state constrained arguments

2022/01/31 by Ioana Ciotir, Ciotir, Ioana, Dan Goreac +3
Computer Science · Economics, Econometrics and Finance · #Advanced Mathematical Modeling in Engineering #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2201.13082

Abstract

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.

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