Stabilization of Solutions of the Stochastic Dynamical Wentzell System on the Half-Sphere with Its Edge

The paper considers the problem of stabilizing the solutions of the deterministic and stochastic Wenzell equations, which describe the dynamics of the filtering fluid in the hemisphere and at its boundary. First, the question of stability and instability of solutions of a deterministic system of Wenzell equations in terms of stable and unstable invariant spaces is examined. For solutions lying in an unstable invariant space, the stabilization problem is solved based on the principle of feedback. The results are then applied to the stochastic system of Wenzell equations. Here the Nelson - Glyclih derivative is considered as a derivative, and the solution is a stochastic process.