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Mat. Zametki, 1998, Volume 63, Issue 6, Pages 835–846 (Mi mz1353)  

This article is cited in 8 scientific papers (total in 8 papers)

Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases

A. A. Zlotnik, A. A. Amosov

Moscow Power Engineering Institute (Technical University)

Abstract: Nonhomogeneous initial boundary value problems for a specific quasilinear system of equations of composite type are studied. The system describes the one-dimensional motion of a viscous perfect polytropic gas. We assume that the initial data belong to the spaces $L_\infty(\Omega)$ or $L_2(\Omega)$ and the problems under consideration have generalized solutions only. For such solutions, a theorem on strong stability is proved, i.e., estimates for the norm of the difference of two solutions are expressed in terms of the sums of the norms of the differences of the corresponding data. Uniqueness of generalized solutions is a simple consequence of this theorem.


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English version:
Mathematical Notes, 1998, 63:6, 736–746

Bibliographic databases:

UDC: 517.958+533.7
Received: 27.06.1996

Citation: A. A. Zlotnik, A. A. Amosov, “Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases”, Mat. Zametki, 63:6 (1998), 835–846; Math. Notes, 63:6 (1998), 736–746

Citation in format AMSBIB
\by A.~A.~Zlotnik, A.~A.~Amosov
\paper Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 6
\pages 835--846
\jour Math. Notes
\yr 1998
\vol 63
\issue 6
\pages 736--746

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    This publication is cited in the following articles:
    1. Zlotnik A. Amosov A., “Weak Solutions to Viscous Heat-Conducting Gas M-Equations with Discontinuous Data: Global Existence, Uniqueness, and Regularity”, Navier-Stokes Equations: Theory and Numerical Methods, Lecture Notes in Pure and Applied Mathematics, 223, ed. Salvi R., Marcel Dekker, 2002, 141–158  mathscinet  zmath  isi
    2. A. A. Zlotnik, Sun Jiang, “Well-Definedness of the Cauchy Problem for the One-Dimensional Equations of Viscous Heat Conducting Gas with Initial Data from Lebesgue Spaces”, Math. Notes, 73:5 (2003), 730–735  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Jiang, S, “Global well-posedness of the Cauchy problem for the equations of a one-dimensional viscous heat-conducting gas with Lebesgue initial data”, Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 134 (2004), 939  crossref  mathscinet  zmath  isi
    4. A. A. Zlotnik, “Weak Solutions to the Equations of Motion of Viscous Compressible Reacting Binary Mixtures: Uniqueness and Lipschitz-Continuous Dependence on Data”, Math. Notes, 75:2 (2004), 278–283  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Fan, JS, “Stability of weak solutions to the compressible Navier–Stokes equations in bounded annular domains”, Mathematical Methods in the Applied Sciences, 31:2 (2008), 179  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Fan J. Jiang S. Nakamura G., “Stability of Weak Solutions to Equations of Magnetohydrodynamics with Lebesgue Initial Data”, J. Differ. Equ., 251:8 (2011), 2025–2036  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    7. Fan J., Huang Sh., Li F., “Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vacuum”, Kinet. Relat. Mod., 10:4 (2017), 1035–1053  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Dou Ch., Xu Ya., 4Th International Conference on Advances in Energy Resources and Environment Engineering, IOP Conf. Ser. Earth Envir. Sci., IOP Conference Series-Earth and Environmental Science, 237, IOP Publishing Ltd, 2019  crossref  isi
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