?
Properties of an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture
Doklady Mathematics . 2021. Vol. 104. No. 3. P. 340–346.
For an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture, we give an entropy balance equation with a nonnegative entropy production in the presence of diffusion fluxes. We also derive the existence, uniqueness, and L^2 -dissipativity of weak solutions to an initial-boundary value problem for the system linearized at a constant solution. Additionally, the Petrovskii parabolicity and local-in-time classical unique solvability of the Cauchy problem for the quasi-gasdynamic system itself are established.
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2021 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Shestoperov A. I., Fomina E. V., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., International Frequency Sensor Association (IFSA) Publishing, 19-21 February 2025 Granada, Spain 2025 P. 172–176
The paper presents models for an innovative fully robotic warehouse for storing boxed goods. A discrete multiagent simulation of the movement of shuttles in a warehouse for a given sequence of pallet shipments has been implemented. Different strategies for placement of boxes in various areas of a warehouse are evaluated, as well as optimal routing ...
Added: June 26, 2026
Fedorov Timofey, Moscow Mathematical Journal 2026 Vol. 26 No. 1 P. 73–85
We obtain a complete list of smooth projective threefolds over C for which the dimension of the space of vanishing cycles (in H2(Y,Q) of the smooth hyperplane section Y) equals 2. We also obtain a complete list of rank 2 very ample vector bundles E on smooth projective surfaces with c2(E)=3. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций, включенных в программу весенней математической школы. ...
Added: June 25, 2026
Fedchenko A., Journal of Mathematical Sciences 2023 Vol. 270 No. 6 P. 815–826
We consider regularizations of systems of equations for a multicomponent gas mixture dynamics in the barotropic multi-velocity and one-velocity cases. Energy balance equations are derived for them.
For the system of equations in the one-velocity case, the system linearized on a constant solution is studied, and, for the weak solutions to the initial-boundary value problem with ...
Added: May 11, 2023
A. A. Zlotnik, T. A. Lomonosov, Computational Mathematics and Mathematical Physics (Germany) 2022 Vol. 62 No. 11 P. 1817–1837
We study an explicit two-level finite difference scheme on staggered meshes, with a quasi-hydrodynamic regularization, for 1D barotropic gas dynamics equations. We derive both necessary conditions and sufficient conditions close to them, for $L^2$-dissipativity of solutions to the Cauchy problem linearized on a constant solution, for any background Mach number $M$. We apply the spectral approach and analyze matrix ...
Added: October 18, 2022
Zlotnik A.A., Fedchenko A.S., Differential Equations 2022 Vol. 58 No. 3 P. 341–356
We study a quasihydrodynamic system of equations for a homogeneous (with common velocity and temperature) multicomponent gas mixture in the absence of chemical reactions with a common regularizing velocity. For this system, we derive an entropy balance equation with nonnegative entropy production in the presence of diffusion flows of the mixture components. In the absence of diffusion ...
Added: May 13, 2022
Zlotnik A., Fedchenko A., Mathematical Methods in the Applied Sciences 2022 Vol. 45 No. 15 P. 8906–8927
Two aggregated regularized systems of equations for a multicomponent homogeneous gas mixture are considered.
An entropy balance equation with a non-negative entropy production is derived for them in the presence of diffusion fluxes. The existence, uniqueness and $L^2$-dissipativity of weak solutions to an initial-boundary value problem for the systems linearized on a constant solution are established. The Petrovskii ...
Added: January 12, 2022
Zlotnik A., Symmetry 2021 Vol. 13 No. 11 Article 2184
We deal with 2D and 3D barotropic gas dynamics system of equations with two viscous regularizations: so-called quasi-gas dynamics (QGD) and quasi-hydrodynamics (QHD) ones. The system is linearized on a constant solution with any velocity, and an explicit two-level in time and symmetric three-point in each spatial direction finite-difference scheme on the uniform rectangular mesh is ...
Added: November 12, 2021
Zlotnik A.A., Lomonosov T.A., Mathematical Models and Computer Simulations 2021 Vol. 13 No. 6 P. 1097–1108
Explicit two-level difference schemes on staggered meshes are studied for two well-known
regularizations of 1D barotropic gas dynamics equtions, including schemes with discretization in
x with the property of total energy dissipation. The criteria of L^2-dissipativity in the Cauchy problem
are derived for their linearizations on a constant solution with zero background velocity. The criteria for
schemes on nonstaggered and staggered ...
Added: September 21, 2021
Zlotnik A., Lomonosov T., Математическое моделирование 2021 Т. 33 № 5 С. 16–34
We study explicit two-level finite-difference schemes on staggered meshes for two known regularizations of 1D barotropic gas dynamics equations including schemes with discretizations in x that possess the dissipativity property with respect to the total energy. We derive criterions of L^2-dissipativity in the Cauchy problem for their linearizations at a constant solution with zero background ...
Added: April 1, 2021
Zlotnik A., , in: Differential and Difference Equations with Applications. ICDDEA 2019, Lisbon, Portugal, July 1–5Vol. 333.: Springer, 2020. P. 53–67.
We study an explicit two-level in time and three-point symmetric in space finite-difference scheme for 1D barotropic and full gas dynamics systems of equations. The scheme is a linearization at a constant background solution (with an arbitrary velocity) of finite-difference schemes with general viscous regularization. We enlarge recently proved sufficient conditions (on the Courant-like number) for $L^2$-dissipativity in ...
Added: November 1, 2020
А. А. Злотник, Т. А. Ломоносов, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2020 Т. 492 № 1 С. 31–37
We study an explicit two-level symmetric in space finite-difference scheme for the multi\-di\-men\-si\-onal barotropic gas dynamics system of equations with quasi-gasdynamic regulari\-za\-tion linearized at a constant solution (with arbitrary velocity). A criterion and both necessary and sufficient conditions for the $L^2$-dissipativity of the solutions to the Cauchy problem for the scheme are derived by the spectral ...
Added: March 4, 2020
Zlotnik A., Lomonosov T., Applied Mathematics Letters 2020 Vol. 103 Article 106198
We study an explicit in time and symmetric in space finite-difference scheme with a kinetic regularization for the 2D and 3D gas dynamics system of equations linearized at a constant solution (with any velocity). We derive both necessary and sufficient conditions for $L^2$-dissipativity of the Cauchy problem for the scheme by the spectral method. The Courant number ...
Added: December 21, 2019
Elizarova T. G., Zlotnik A.A., Shil’nikov E. V., Computational Mathematics and Mathematical Physics 2019 Vol. 59 No. 11 P. 1832–1847
Regularized equations for binary mixtures of viscous compressible gases (in the absence of chemical reactions) are considered. Two new simpler systems of equations are constructed for the case of a homogeneous mixture, when the velocities and temperatures of the components coincide. In the case of moderately rarefied gases, such a system is obtained by aggregating previously derived general equations ...
Added: October 22, 2019
Elizarova T., Zlotnik A., AIP Conference Proceedings 2020 Vol. 2293 No. 1 P. 210016-1–210016-4
We consider binary gas mixture flows with viscous compressible components in the absence of chemical reactions.
We aggregate the previously derived regularized equations for inhomogeneous mixtures and thus derive new simpler regularized equations for homogeneous ones (i.e., with the common velocity and temperature). The entropy balance equation with the non-negative entropy production is stated for the new equations. They ...
Added: July 21, 2019
Zlotnik A.A., Lomonosov T.A., Computational Mathematics and Mathematical Physics 2019 Vol. 59 No. 3 P. 452–464
Explicit two-level in time and symmetric in space finite-difference schemes constructed by approximating the 1D barotropic quasi-gas-/quasi-hydrodynamic systems of equations are studied. The schemes are linearized about a constant solution with a nonzero velocity, and, for them, necessary and sufficient conditions for the L2-dissipativity of solutions to the Cauchy problem are derived depending on the Mach number. These conditions ...
Added: March 11, 2019
Zlotnik A., Applied Mathematics Letters 2019 Vol. 92 P. 115–120
We deal with an explicit finite-difference scheme with a regularization for the 1D gas dynamics equations linearized at the constant solution. The sufficient condition on the Courant number for the $L^2$-dissipativity of the scheme is derived in the case of the Cauchy problem and a non-uniform spatial mesh. The energy-type technique is developed to this end, and ...
Added: January 20, 2019