Parabolicity of the Quasi-Gasdynamic System of Equations,Its Hyperbolic Second-Order Modification, and the Stability of Small Perturbations for Them

A. A. Zlotnik; B. N. Chetverushkin

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Parabolicity of the Quasi-Gasdynamic System of Equations,Its Hyperbolic Second-Order Modification, and the Stability of Small Perturbations for Them

机译：拟气动方程组的抛物线性，其双曲型二阶修正及其小扰动的稳定性

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Criteria (necessary and sufficient conditions) for the Petrovskii parabolicity of the quasi-gas-dynamic system of equations with an improved description of heat conduction are derived. A modifiedquasi-gasdynamic system containing second derivatives with respect to both spatial and time variablesis proposed. Necessary and sufficient conditions for its hyperbolicity are deduced. For both systems, thestability of small perturbations against a constant background is analyzed and estimates that are uniformon an infinite time interval are given for relative perturbations in the Cauchy problem and the initial—boundary value problem for the corresponding linearized systems. Similar results are also established inthe barotropic case with the general equation of state p = p(p).

机译：推导了准气体动力学方程组的Petrovskii抛物线的准则（必要条件和充分条件），并改进了热传导描述。提出了一种改进的准气动力系统，该系统包含关于空间和时间变量的二阶导数。推导出了其双曲性的充要条件。对于这两个系统，分析了在恒定背景下的小扰动的稳定性，并给出了柯西问题和相应线性化系统的初边值问题的相对扰动在无限时间间隔内一致的估计。在正压情况下，状态状态的一般方程为p = p（p），也建立了类似的结果。

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《Computational mathematics and mathematical physics》 |2008年第3期|共27页
作者
A. A. Zlotnik; B. N. Chetverushkin;
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正文语种 eng
中图分类计算数学;
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gas dynamics; quasi-gasdynamic system of equations; second-order parabolic and hyper-bolic systems; principal symbol; stability of small perturbations; symmetrization; Fourier transform;

机译：气体动力学;方程的准气体动力学系统;二阶抛物和双曲系统;本征;小扰动的稳定性;对称化;傅立叶变换;

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专利

1. 高阶非线性双曲型抛物型耦合方程组的周期边界问题和初值问题 [J] . 陈国旺数学季刊：英文版 . 1990,第004期
2. Parabolicity of the Quasi-Gasdynamic System of Equations,Its Hyperbolic Second-Order Modification, and the Stability of Small Perturbations for Them [J] . A. A. Zlotnik, B. N. Chetverushkin Computational mathematics and mathematical physics . 2008,第3期

机译：拟气动方程组的抛物线性，其双曲型二阶修正及其小扰动的稳定性
3. Stability of Implicit Difference Schemes for a Linearized Hyperbolic Quasi-Gasdynamic System of Equations [J] . Zlotnik A. A., Chetverushkin B. N. Differential equations: A translation of differensial'nye uraveniya . 2020,第7期

机译：线性化双曲拟气动力系统的隐式差分方案的稳定性
4. The stability of difference schemes of second-order of accuracy for hyperbolic-parabolic equations [J] . Ashyralyev A, Yurtsever HA Computers & mathematics with applications . 2006,第3a4期

机译：双曲-抛物方程的二阶精度差分格式的稳定性
5. Mathematical Model in the Form of a Loaded Second-Order Parabolic-Hyperbolic Equation with a Singular Coefficient [C] . Vadim N. Lesev, Anna O. Zheldasheva, Oksana I. Bzheumikhova, IEEE International Conference on Quality Management, Transport and Information Security, Information Technologies . 2018

机译：具有奇异系数的二阶抛物线-双曲型方程形式的数学模型
6. Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations. [D] . Al-Islam, Najja Shakir. 2009

机译：某些非线性双曲型二阶偏微分方程组的伪几乎周期解。
7. A Perturbation Series for Cauchys Problem for Higher-Order Abstract Parabolic Equations [O] . J. A. Donaldson, R. Hersh 1970

机译：高阶抽象抛物方程的柯西问题的摄动级数
8. The stability of difference schemes of second-order of accuracy for hyperbolic-parabolic equations [O] . Ashyralyev A., Yurtsever H.A. 2006

机译：双曲-抛物方程的二阶精度差分格式的稳定性
9. Error Estimates for Piecewise Perturbation Series Solutions of Parabolic and Hyperbolic Equations [R] . Smooke, M. D. 1980

机译：抛物型和双曲型方程的分段扰动级数解的误差估计

Parabolicity of the Quasi-Gasdynamic System of Equations,Its Hyperbolic Second-Order Modification, and the Stability of Small Perturbations for Them

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