RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

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

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.

DOI: https://doi.org/10.4213/mzm1353

Full text: PDF file (239 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.958+533.7

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
\Bibitem{ZloAmo98} \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 \mathnet{http://mi.mathnet.ru/mz1353} \crossref{https://doi.org/10.4213/mzm1353} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1679215} \zmath{https://zbmath.org/?q=an:0917.35109} \transl \jour Math. Notes \yr 1998 \vol 63 \issue 6 \pages 736--746 \crossref{https://doi.org/10.1007/BF02312766} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000076726600025} 

• http://mi.mathnet.ru/eng/mz1353
• https://doi.org/10.4213/mzm1353
• http://mi.mathnet.ru/eng/mz/v63/i6/p835

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
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
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
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
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
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
•  Number of views: This page: 264 Full text: 108 References: 46 First page: 1