Properties of an Aggregated Quasi-Gasdynamic System of Equations for a Homogeneous Gas Mixture

Злотник, А. А.; Fedchenko, A. S.

doi:10.1134/s1064562421060193

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…The following lemmas are similar to those deduced recently in [17] (the difference case) and [34] (the differential case).…”

Section: § 1 Introductionsupporting

confidence: 76%

Properties and errors of second-order parabolic and hyperbolic perturbations of a first-order symmetric hyperbolic system

Zlotnik,

Chetverushkin

2023

Sb. Math.

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The Cauchy problems are studied for a first-order multidimensional symmetric linear hyperbolic system of equations with variable coefficients and its singular perturbations that are second-order strongly parabolic and hyperbolic systems of equations with a small parameter $\tau>0$ multiplying the second derivatives with respect to $x$ and $t$. The existence and uniqueness of weak solutions of all three systems and $\tau$-uniform estimates for solutions of systems with perturbations are established. Estimates for the difference of solutions of the original system and the systems with perturbations are given, including ones of order $O(\tau^{\alpha/2})$ in the norm of $C(0,T;L^2(\mathbb{R}^n))$, for an initial function $\mathbf w_0$ in the Sobolev space $H^\alpha(\mathbb{R}^n)$, $\alpha=1,2$, or the Nikolskii space $H_2^{\alpha}(\mathbb{R}^n)$, $0<\alpha<2$, $\alpha\neq 1$, and under appropriate assumptions on the free term of the first-order system. For ${\alpha=1/2}$ a wide class of discontinuous functions $\mathbf w_0$ is covered. Estimates for derivatives of any order with respect to $x$ for solutions and of order $O(\tau^{\alpha/2})$ for their differences are also deduced. Applications of the results to the first-order system of gas dynamic equations linearized at a constant solution and to its perturbations, namely, the linearized second-order parabolic and hyperbolic quasi-gasdynamic systems of equations, are presented. Bibliography: 34 titles.

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“…The following lemmas are similar to those deduced recently in [17] (the difference case) and [34] (the differential case).…”

Section: § 1 Introductionsupporting

confidence: 76%

Properties and errors of second-order parabolic and hyperbolic perturbations of a first-order symmetric hyperbolic system

Zlotnik,

Chetverushkin

2023

Sb. Math.

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“…see [19]. A similar bound holds for the initial-boundary value problem supplemented with the homogeneous Dirichlet boundary condition as well, see also [21]. These bounds became the starting point for the subsequent analysis of the dissipativity property for the approximating explicit symmetric difference scheme.…”

mentioning

confidence: 76%

“…Let w ∈ H h . Note that A ≥ 0 due to (21) and thus λ ≥ 0. Applying the Cauchy-Schwarz inequality and then inequalities (21) and A 2 ≤ λA, we derive the bounds…”

Section: If the Operatorsmentioning

confidence: 99%

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

Злотник

2023

DCDS-B

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<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M2">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-dissipativity are derived for the first time by the energy method. For the Cauchy problem on the uniform mesh, recent both necessary conditions and sufficient conditions for the <inline-formula><tex-math id="M3">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-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.</p>

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On Second-Order Parabolic and Hyperbolic Perturbations of a First-Order Hyperbolic System

Злотник

Четверушкин

2022

Dokl. Math.

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Properties of an Aggregated Quasi-Gasdynamic System of Equations for a Homogeneous Gas Mixture

Cited by 4 publications

References 7 publications

Properties and errors of second-order parabolic and hyperbolic perturbations of a first-order symmetric hyperbolic system

Properties and errors of second-order parabolic and hyperbolic perturbations of a first-order symmetric hyperbolic system

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

On Second-Order Parabolic and Hyperbolic Perturbations of a First-Order Hyperbolic System

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