Stabilization of Solutions for the Wentzell Stochastic Dynamical System in a Circle and on Its Boundary

Abstract

The paper considers the problem of stabilizing the solutions of the deterministic and stochastic Wenzel equations, which describe the filtration of a liquid in a circle and on its boundary. The authors address the issue of exponential stability and instability of the deterministic Wenzell equations solutions. They consider different signs of the parameters that describe the medium and the properties of the liquid. The instability gives rise to solving the problem of stabilization using a feedback loop. The obtained results are used in the stochastic Wenzell equations. The Nelson–Gleich derivative is considered, and a stochastic process is a solution.