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## Conditions for L^2-dissipativity of an explicit symmetric finite-difference scheme for linearized 2D and 3D gas dynamics equations with a regularization

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 problem on the uniform mesh, recent both necessary conditions and sufficient conditions for the $L^2$-dissipativity in the spectral method are improved. A new form for the relaxation parameter is suggested which guarantees that the Courant-type number is uniformly bounded from above and below with respect to the mesh and the Mach number.

Zlotnik Alexander, Discrete and Continuous Dynamical Systems - Series B (США) 2022

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 Alexander, Discrete and Continuous Dynamical Systems - Series B 2022

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., 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

Samovol V. S., Математические заметки 2012 Т. 92 № 6 С. 912-927

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of the linearized system has two pure imaginary eigenvalues, all other eigenvalues lying outside the imaginary axis. The problem of local finitely smooth equivalence of such systems is studied. ...

Added: December 13, 2012

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

G.F. Helminck, Poberezhny V. A., S.V. Polenkova, 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

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

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

Demina M.V., Sinelshchikov D., International Journal of Non-Linear Mechanics 2020 Vol. 121 Article 103439

We consider integrability properties of a family of forced nonlinear oscillators, which generalizes the Liénardequation. We demonstrate that some forced oscillators with previously known first integrals can be linearizedvia certain nonlocal transformations. Furthermore, we show that the whole family of Liénard (𝑛,𝑛+1) equations with arbitrary external forcing admits a first integral. We study in detail ...

Added: February 17, 2020

Zlotnik A., Lomonosov T., Доклады Академии наук 2018 Т. 482 № 4 С. 375-380

Изучается явная двухслойная по времени и симметричная по пространству разностная схема, аппроксимирующая 1D квазигазодинамическую систему уравнений. Она линеаризуется на постоянном решении и для нее выводятся новые как необходимые, так и достаточные условия $L^2$-диссипативности решений задачи Коши, в том числе впервые при ненулевой фоновой скорости в зависимости от числа Маха.
Показано, что можно обеспечить независимость условия на число ...

Added: May 21, 2018

Protasov V., Calcolo 2019 Vol. 56 No. 2 P. 1-11

Multiple Perron eigenvectors of non-negative matrices occur in applications, where
they often become a source of trouble. A usual way to avoid it and to make the
Perron eigenvector simple is a regularization of matrix: an initial non-negative matrix
A is replaced by A + "M, where M is a strictly positive matrix and " > 0 is ...

Added: June 12, 2019

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

Samovol V. S., Математические заметки 2012 Т. 92 № 5 С. 731-746

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of the linearized system has two pure imaginary eigenvalues, all other eigenvalues lying outside the imaginary axis. The reducibility of such systems to pseudonormal form is studied. ...

Added: December 13, 2012

Zlotnik A.A., B.N. Chetverushkin, 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

B. N. Chetverushkin, Zlotnik A.A., Russian Journal of Mathematical Physics 2017 Vol. 24 No. 3 P. 299-309

We study a multidimensional hyperbolic quasi-gasdynamic (HQGD) system of equations containing terms with a regularizing parameter $\tau>0$ and 2nd order space and time derivatives; the body force is taken into account. We transform it to the form close to the compressible Navier-Stokes system of equations. Then we derive the entropy balance equation and show that ...

Added: July 19, 2017

Veretennikova M., Alla Sikorskii, Michael Boivin, RUDN, 2017

In this research we compare the performance of different data mining techniques in the analysis of electroencephalogram (EEG) data. We study the question od predicting post-comatose neuro-developmental scores based mainly on statistical features of the EEG recordings. We compare results from applying different data mining techniques, such as the Elastic Net, Lasso, Gaussian Support Vector ...

Added: October 31, 2019

Evtushenko Yu. G., A. I. Golikov, Proceedings of the Steklov Institute of Mathematics 2015 Vol. 289 P. 102-110

The paper provides some examples of mutually dual unconstrained optimization problems originating from regularization problems for systems of linear equations and/or inequalities. The solution of each of these mutually dual problems can be found from the solution of the other problem by means of simple formulas. Since mutually dual problems have different dimensions, it is ...

Added: October 6, 2016

Litvin Y. V., Игорь Вячеслвович Абрамов, Технологии техносферной безопасности 2016 № 66

Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...

Added: August 27, 2016

Furmanov K. K., I. M. Nikol'skii, Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Arzhantsev I., Journal of Lie Theory 2000 Vol. 10 No. 2 P. 345-357

Added: July 8, 2014

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Min Namkung, Kwon Younghun, Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala: University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016