Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (6)

Search Parameters:
Authors = Gennadii Alekseev ORCID = 0000-0003-2570-3696

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
42 pages, 702 KiB  
Article
Stability Estimates of Optimal Solutions for the Steady Magnetohydrodynamics-Boussinesq Equations
by Gennadii Alekseev and Yuliya Spivak
Mathematics 2024, 12(12), 1912; https://doi.org/10.3390/math12121912 - 20 Jun 2024
Cited by 2 | Viewed by 1220
Abstract
This paper develops the mathematical apparatus of studying control problems for the stationary model of magnetic hydrodynamics of viscous heat-conducting fluid in the Boussinesq approximation. These problems are formulated as problems of conditional minimization of special cost functionals by weak solutions of the [...] Read more.
This paper develops the mathematical apparatus of studying control problems for the stationary model of magnetic hydrodynamics of viscous heat-conducting fluid in the Boussinesq approximation. These problems are formulated as problems of conditional minimization of special cost functionals by weak solutions of the original boundary value problem. The model under consideration consists of the Navier–Stokes equations, the Maxwell equations without displacement currents, the generalized Ohm’s law for a moving medium and the convection-diffusion equation for temperature. These relations are nonlinearly connected via the Lorentz force, buoyancy force in the Boussinesq approximation and convective heat transfer. Results concerning the existence and uniqueness of the solution of the original boundary value problem and of its generalized linear analog are presented. The global solvability of the control problem under study is proved and the optimality system is derived. Sufficient conditions on the data are established which ensure local uniqueness and stability of solutions of the control problems under study with respect to small perturbations of the cost functional to be minimized and one of the given functions. We stress that the unique stability estimates obtained in the paper have a clear mathematical structure and intrinsic beauty. Full article
(This article belongs to the Special Issue Mathematical Problems in Fluid Mechanics)
►▼ Show Figures

Figure 1

24 pages, 553 KiB  
Article
Inhomogeneous Boundary Value Problems for the Generalized Boussinesq Model of Mass Transfer
by Gennadii Alekseev and Olga Soboleva
Mathematics 2024, 12(3), 391; https://doi.org/10.3390/math12030391 - 25 Jan 2024
Cited by 4 | Viewed by 1192
Abstract
We consider boundary value problems for a nonlinear mass transfer model, which generalizes the classical Boussinesq approximation, under inhomogeneous Dirichlet boundary conditions for the velocity and the substance’s concentration. It is assumed that the leading coefficients of viscosity and diffusion and the buoyancy [...] Read more.
We consider boundary value problems for a nonlinear mass transfer model, which generalizes the classical Boussinesq approximation, under inhomogeneous Dirichlet boundary conditions for the velocity and the substance’s concentration. It is assumed that the leading coefficients of viscosity and diffusion and the buoyancy force in the model equations depend on concentration. We develop a mathematical apparatus for studying the inhomogeneous boundary value problems under consideration. It is based on using a weak solution of the boundary value problem and on the construction of liftings of the inhomogeneous boundary data. They remove the inhomogeneity of the data and reduce initial problems to equivalent homogeneous boundary value problems. Based on this apparatus we will prove the theorem of the global existence of a weak solution to the boundary value problem under study and establish important properties of the solution. In particular, we will prove the validity of the maximum principle for the substance’s concentration. We will also establish sufficient conditions for the problem data, ensuring the local uniqueness of weak solutions. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
►▼ Show Figures

Figure 1

29 pages, 626 KiB  
Article
Analysis of Control Problems for Stationary Magnetohydrodynamics Equations under the Mixed Boundary Conditions for a Magnetic Field
by Gennadii Alekseev
Mathematics 2023, 11(12), 2610; https://doi.org/10.3390/math11122610 - 7 Jun 2023
Cited by 2 | Viewed by 4258
Abstract
The optimal control problems for stationary magnetohydrodynamic equations under the inhomogeneous mixed boundary conditions for a magnetic field and the Dirichlet condition for velocity are considered. The role of controls in the control problems under study is played by normal and tangential components [...] Read more.
The optimal control problems for stationary magnetohydrodynamic equations under the inhomogeneous mixed boundary conditions for a magnetic field and the Dirichlet condition for velocity are considered. The role of controls in the control problems under study is played by normal and tangential components of the magnetic field given on different parts of the boundary and by the exterior current density. Quadratic tracking-type functionals for velocity, magnetic field or pressure are taken as cost functionals. The global solvability of the control problems under consideration is proved, an optimality system is derived and, based on its analysis, a mathematical apparatus for studying the local uniqueness and stability of the optimal solutions is developed. On the basis of the developed apparatus, the local uniqueness of solutions of control problems for specific cost functionals is proved, and stability estimates of optimal solutions are established. Full article
(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)
►▼ Show Figures

Figure 1

17 pages, 1324 KiB  
Article
Optimization Method for Solving Cloaking and Shielding Problems for a 3D Model of Electrostatics
by Gennadii Alekseev and Alexey Lobanov
Mathematics 2023, 11(6), 1395; https://doi.org/10.3390/math11061395 - 13 Mar 2023
Cited by 1 | Viewed by 1737
Abstract
Inverse problems for a 3D model of electrostatics, which arise when developing technologies for designing electric cloaking and shielding devices, are studied. It is assumed that the devices being designed to consist of a finite number of concentric spherical layers filled with homogeneous [...] Read more.
Inverse problems for a 3D model of electrostatics, which arise when developing technologies for designing electric cloaking and shielding devices, are studied. It is assumed that the devices being designed to consist of a finite number of concentric spherical layers filled with homogeneous anisotropic or isotropic media. A mathematical technique for solving these problems has been developed. It is based on the formulation of cloaking or shielding problems in the form of inverse problems for the electrostatic model under consideration, reducing the latter problems to finite-dimensional extremum problems, and finding their solutions using one of the global minimization methods. Using the developed technology, the inverse problems are replaced by control problems, in which the role of controls is played by the permittivities of separate layers composing the device being designed. To solve them, a numerical algorithm based on the particle swarm optimization method is proposed. Important properties of optimal solutions are established, one of which is the bang-bang property. It is shown on the base of the computational experiments that cloaking and shielding devices designed using the developed algorithm have the simplicity of technical implementation and the highest performance in the class of devices under consideration. Full article
(This article belongs to the Special Issue Theoretical Research and Computational Applications in Fluid Dynamics)
►▼ Show Figures

Figure 1

20 pages, 364 KiB  
Article
Theoretical Analysis of Boundary Value Problems for Generalized Boussinesq Model of Mass Transfer with Variable Coefficients
by Gennadii Alekseev and Roman Brizitskii
Symmetry 2022, 14(12), 2580; https://doi.org/10.3390/sym14122580 - 6 Dec 2022
Cited by 15 | Viewed by 1696
Abstract
A boundary value problem is formulated for a stationary model of mass transfer, which generalizes the Boussinesq approximation in the case when the coefficients in the model equations can depend on the concentration of a substance or on spatial variables. The global existence [...] Read more.
A boundary value problem is formulated for a stationary model of mass transfer, which generalizes the Boussinesq approximation in the case when the coefficients in the model equations can depend on the concentration of a substance or on spatial variables. The global existence of a weak solution of this boundary value problem is proved. Some fundamental properties of its solutions are established. In particular, the validity of the maximum principle for the substance’s concentration has been proved. Sufficient conditions on the input data of the boundary value problem under consideration, which ensure the local existence of the strong solution from the space H2, and conditions that ensure the conditional uniqueness of the weak solution with additional property of smoothness for the substance’s concentration are established. Full article
(This article belongs to the Special Issue Mathematical Fluid Dynamics and Symmetry)
15 pages, 323 KiB  
Article
Solvability Analysis of a Mixed Boundary Value Problem for Stationary Magnetohydrodynamic Equations of a Viscous Incompressible Fluid
by Gennadii Alekseev and Roman V. Brizitskii
Symmetry 2021, 13(11), 2088; https://doi.org/10.3390/sym13112088 - 4 Nov 2021
Cited by 5 | Viewed by 1762
Abstract
We investigate the boundary value problem for steady-state magnetohydrodynamic (MHD) equations with inhomogeneous mixed boundary conditions for a velocity vector, given the tangential component of a magnetic field. The problem represents the flow of electrically conducting viscous fluid in a 3D-bounded domain, which [...] Read more.
We investigate the boundary value problem for steady-state magnetohydrodynamic (MHD) equations with inhomogeneous mixed boundary conditions for a velocity vector, given the tangential component of a magnetic field. The problem represents the flow of electrically conducting viscous fluid in a 3D-bounded domain, which has the boundary comprising several parts with different physical properties. The global solvability of the boundary value problem is proved, a priori estimates of the solutions are obtained, and the sufficient conditions on data, which guarantee a solution’s local uniqueness, are determined. Full article
(This article belongs to the Special Issue Applied Mathematics and Fluid Dynamics)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop