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On dissipativity of linearized 1d quasi-gasdynamic system of equations and its difference approximation for general equations of state
Lobachevskii Journal of Mathematics. 2025. Vol. 46. No. 11. P. 5718–5731.
We deal with the 1D quasi-gasdynamic (QGD) system of equations and a two-level explicit in time and three-point symmetric in space conservative difference scheme that approximates it, in the case of general equations of state.
Both the QGD system and scheme are linearized at any constant background solution (with non-zero or zero velocity). Matrices of their convective and dissipative terms are the same, and after respective scaling, they both become symmetric and depend mainly on the background ``signed'' Mach number and the ratio of the specific heats as well as the QGD parameters. Moreover, their form is almost the same as in the previously studied basic particular case of the perfect polytropic gas. This allows us to extend results on $L^2$-dissipativity of the QGD system and the scheme to the general case.
Springer, 2026.
The book presents the proceedings of the 13th International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA 2024), held at Intelligent Systems Research Group (ISRG), London Metropolitan University, London, United Kingdom, during June 6–7, 2025. Researchers, scientists, engineers and practitioners exchange new ideas and experiences in the domain of intelligent computing theories with ...
Added: June 8, 2026
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
Medvedev T. V., Pochinka O., Chaos 2026 Vol. 36 No. 6 Article 063107
We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...
Added: June 4, 2026
Seul: PMLR, 2026.
Added: June 4, 2026
Kazakov A., Mints D., Petrova I. et al., Chaos 2026 Vol. 36 No. 6 Article 063112
We study hyperbolic chaotic dynamics for maps of a two-dimensional torus. We introduce a two-parameter family of diffeomorphisms which, as we show, demonstrates all types of hyperbolic chaotic dynamics that can appear in the two-dimensional case. In addition, we describe all the bifurcations responsible for the transitions between these chaotic regimes. ...
Added: June 4, 2026
Nozdrinova E., Pochinka O., Shmukler V., Математический сборник 2026 Т. 217 № 6 С. 71–89
Гомеоморфизмы топологических пространств называются эквивалентными по надстройке, если надстройки над ними топологически эквивалентны. В частности, топологически сопряженные гомеоморфизмы эквивалентны по надстройке. Известно, что для гомологически неприводимых гомеоморфизмов их топологическая сопряженность является необходимым и достаточным условием их эквивалентности по надстройке. Тогда как инварианты топологической сопряженности гомологически приводимых гомеоморфизмов во многих случаях являются избыточными для эквивалентности по ...
Added: June 3, 2026
Gnetov F., Konakov V., Успехи математических наук 2026 Т. 81 № 3 (489) С. 161–162
Пусть M обозначает симметрическое пространство некомпактного типа ранга 1. Опираясь на фундаментальную работу [1], в [2] было показано, что плотность соответствующим образом нормированной суммы независимых Hn-значных случайных величин, определенная через сложение Мёбиуса в модели шара Пуанкаре, сходится к фундаментальному решению соответствующего уравнения теплопроводности. Пределом являлся нормальный закон на Hn, соответствующий ядру теплопроводности, определяемому оператором Лапласа–Бельтрами. ...
Added: June 2, 2026
Silakov D., Системный администратор 2026 № 3 С. 28–33
В статье про платформы для разработки открытого ПО в Китае мы рассказали про GitCode – молодой проект, позиционируемый как площадка для разработчиков со всего мира. Сейчас на GitCode размещаются проекты, созданные в КНР, но некоторые из них уже известны и на международной арене. Помочь открытым проектам в становлении, развитии и расширению аудитории призван фонд OpenAtom ...
Added: June 2, 2026
Slivnitsin P., Mylnikov L., Engineering Applications of Artificial Intelligence 2026 Vol. 179 Article 115185
The paper describes a applied artificial intelligence task of recognition-by-components method of real objects based on the recognition of a limited set of primitives or components. The recognition-by-components makes it possible to determine the components, that compose an object, and increase the number of recognizable objects without degrading the recognition quality. Training is performed on ...
Added: May 29, 2026
Zlotnik A., Applied Mathematics Letters 2026 Vol. 173 Article 109793
The system of equations for dynamics of the heterogeneous multicomponent mixtures with the common temperature, pressure and velocity of components is considered in the case of general equations of state. The phase transitions are taken into account. Recently, a kinetic (quasi gasdynamic)-type regularization of the system has been developed and verified in computer simulations in ...
Added: October 23, 2025
Zlotnik A., Lomonosov T., Mathematical Models and Computer Simulations 2025 Vol. 17 No. 3 P. 352–364
A system of four balance differential equations is used to describe dynamics of heteroge neous compressible binary mixtures with stiffened gas equations of state for the mixture’s components, including gas and liquid ones. The main points are its quasi-homogeneous form, which arises as a result of eliminating volume fractions of components from the collection of ...
Added: July 4, 2025
Zlotnik A., Lomonosov T., Doklady Mathematics 2023 Vol. 108 No. 3 P. 443–449
We consider the so-called four-equation model for dynamics of the heterogeneous compressible binary mixtures with the Noble-Abel stiffened-gas equations of state. We exploit its quasi-homogeneous form that arises after excluding the volume concentrations from the sought functions and is based on a quadratic equation for the common pressure of the components. We present new properties ...
Added: March 1, 2024
Zlotnik A., Lomonosov T., Chaos 2023 Vol. 33 No. 11 Article 113128
We deal with the reduced four-equation model for the dynamics of heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations, and with a quadratic equation for the common pressure of the components; this form can be called a quasi-homogeneous form. We prove new properties ...
Added: October 30, 2023
Zlotnik A., Lomonosov T., / Series arXiv "math". 2023. No. 2305.10522.
We deal with the reduced four-equation model for dynamics of the heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations and a quadratic equation for the common pressure of the components, that can be called a quasi-homogeneous form. We prove new properties of ...
Added: May 28, 2023
Zlotnik A., Lomonosov T., Entropy 2023 Vol. 25 No. 1 Article 158
We deal with multidimensional regularized systems of equations for the one-velocity and one-temperature inert gas mixture dynamics consisting of the balance equations for the mass of components and the momentum and total energy of the mixture, with diffusion fluxes between the components as well as the viscosity and heat conductivity terms. The regularizations are kinetically motivated and aimed at ...
Added: January 10, 2023
Zlotnik A.A., Doklady Mathematics 2022 Vol. 106 No. 1 P. 236–242
We study an explicit two-level finite-difference scheme for a linearized multidimensional quasigasdynamic system of equations. For an initial-boundary value problem on a nonuniform rectangular mesh,
sufficient conditions of Courant-type for L^2-dissipativity are derived for the first time by applying the energy
method. For the Cauchy problem on a uniform mesh, both necessary and sufficient conditions for L^2-dissipativity ...
Added: September 7, 2022
Zlotnik A., Discrete and Continuous Dynamical Systems - Series B 2023 Vol. 28 No. 3 P. 1571–1589
We study an explicit two-level in time and symmetric in space finite-difference scheme for a linearized 2D and 3D gas dynamic system of equations with a kinetic-type regularization. For an initial-boundary value problem on any nonuniform rectangular mesh, sufficient Courant-type conditions for the $L^2$-dissipativity are derived for the first time by the energy method. For the Cauchy ...
Added: August 11, 2022
Zlotnik Alexander, Discrete and Continuous Dynamical Systems - Series B (США) 2022 P. 1571–1589
We study an explicit two-level in time and symmetric in space finite-difference scheme for a linearized 2D and 3D gas dynamic system of equations with a kinetic-type regularization. For an initial-boundary value problem on any nonuniform rectangular mesh, sufficient Courant-type conditions for the $L^2$-dissipativity are derived for the first time by the energy method. For the Cauchy ...
Added: June 20, 2022
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
Lomonosov T., Journal of Mathematical Sciences 2021 Vol. 255 No. 4 P. 459–466
We propose an algorithm for linearizing systems of partial differential equations at constant solutions. The algorithm is based on an isomorphism constructed between the ring of linearized functions and the ring of special matrices, which makes it possible to simplify calculations in the process of linearization. The algorithm is illustrated by applying it to the ...
Added: May 9, 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
Helminck G. F., Poberezhny V. A., Polenkova S. V., Theoretical and Mathematical Physics 2020 Vol. 204 No. 3 P. 1140–1153
We show that both the dKP hierarchy and its strict version can be extended to a wider class of deformations satisfying a larger set of Lax equations. We prove that both extended hierarchies have appropriate linearizations allowing a geometric construction of their solutions. ...
Added: October 28, 2020
Sinelshchikov D., Chaos, Solitons and Fractals 2020 Vol. 141 Article 110318
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering the general case of a linearization problem via certain nonlocal transformations. In addition, we show that each equation from the linearizable family admits ...
Added: September 30, 2020
Zlotnik A.A., Chetverushkin B. N., Differential Equations 2020 Vol. 56 No. 7 P. 910–922
We consider a multidimensional hyperbolic quasi-gasdynamic system of differential equations of the second order in time and space linearized at a constant solution (with an arbitrary velocity). For the linearized system with constant coefficients, we study an implicit three-level weighted difference scheme and an implicit two-level vector difference scheme. The important domination property of the operator of ...
Added: July 16, 2020