stochastic dynamic system of Wentzell equations, the Barenblatt–Zheltov–Kochina equation, the Nelson–Gleich derivative, instable solution, solution stabilization.
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.
Author Biographies
Nikita Sergeevich Goncharov, South Ural State University, Chelyabinsk
Senior Lecturer, Equations of Mathematical Physics Department
Olga Gennadevna Kitaeva, South Ural State University, Chelyabinsk
Cand. Sc. (Physics and Mathematics), Associate Professor, Department of Mathematical Physics Equations
Georgiy Anatol'evich Sviridyuk, South Ural State University, Chelyabinsk
Head of Mathematical Physics Non-Classical Equations Research Laboratory
