stochastic dynamic system of Wentzell equations, the Barenblatt–Zheltov–Kochina equation, the Nelson–Gliklikh derivative, solution stabilization
Abstract
The paper considers the problem of numerical investigation of the stabilization processes of solutions of the deterministic and stochastic system of Wentzell equations. A feature of the model under study is the presence of dynamic Wentzell boundary conditions, which describe the interconnected filtration of processes in the internal domain and on its boundary. To solve the problem, it is proposed to use a numerical approach based on the exponential stability and instability of solutions of the deterministic system of Wentzell equations under different signs of the parameters describing the medium and the properties of the fluid. In the case of unstable solutions, the stabilization problem is solved based on a feedback loop. Then, the obtained results are extended to the stochastic system of Wentzell equations. In particular, the paper presents computational experiment demonstrating the effectiveness of the proposed method in modeling stabilization processes in a bounded domain.
Author Biographies
Goncharov Nikita Sergeevich, South Ural State University, Chelyabinsk
Cand. Sc. (Physics and Mathematics), Senior Lecturer, Equations of Mathematical Physics Department
Kitaeva Olga Gennadevna, South Ural State University, Chelyabinsk
Cand. Sc. (Physics and Mathematics), Associate Professor, Department of Mathematical Physics Equations
Sviridyuk Georgiy Anatol'evich, South Ural State University, Chelyabinsk
Dr. Sc. (Physics and Mathematics), Professor, Head of Mathematical Physics Non-Classical Equations Research Laboratory
