This is a preview of subscription content, log in via an institution to check access.
References
A. V. Kazhikhov, “On stabilization of solutions of the initial-boundary problem for equations of barotropic viscous liquid,” Differents. Uravn.,15, No. 4, 662–667 (1979).
V. V. Shelukhin, “Stabilization of a solution of some model problem on the motion of a piston in a viscous gas,” in: Dynamics of Continuous Medium [in Russian], Vol. 33, Novosibirsk (1978), pp. 134–146.
I. Straskraba and A. Valli, “Asymptotic behaviour of the density for one-dimensional Navier-Stokes equations,” Manuscr. Math.,62, No. 4, 401–416 (1988).
A. A. Zlotnik, “On equations of motion of a viscous barotropic gas under the presence of a mass force,” Sib. Mat. Zh.,33, No. 5, 62–79 (1992).
V. V. Shelukhin, “Bounded almost periodic solutions of equations of viscous gas,” in: Dynamics of Continuous Medium [in Russian], Vol. 44, Novosibirsk (1980), pp. 147–163.
A. Valli, “Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method,” Ann. Sc. Norm. Sup. Pisa,10, No. 4, 607–647 (1983).
H. Beirao da Veiga, “Long time behavior for one dimensional motion of a general barotropic fluid,” Arch. Ration. Mech. Anal.,108, No. 2, 141–160 (1989).
S. N. Antontsev, A. V. Kazhikhov, and V. N. Monakhov, Boundary Value Problems of Mechanics of Inhomogeneous Liquids [in Russian], Nauka, Novosibirsk (1983).
P. Secchi and A. Valli, “A free boundary problem for compressible viscous fluids,” J. Reine Angew. Math.,341, 1–31 (1983).
T. Nishida, “Equations of motion of compressible viscous fluids,” in: Patterns and Waves. Qual. Anal. Nonlinear Differ. Equat., Tokyo, Amsterdam (1986), pp. 97–128.
T. Nagasawa, “On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with stress-free conditions,” Quart. Appl. Math.,46, No. 4, 665–679 (1988).
J. Bergh and J. Lofstrom, Interpolation Spaces: an Introduction, Springer-Verlag, Berlin-New York (1976).
A. A. Zlotnik and A. A. Amosov, “Generalized solutions ‘in the large’ of equations of one-dimensional motion of a viscous barotropic gas,” Dokl. Akad. Nauk SSSR,299, No. 6, 1303–1307 (1988).
A. A. Amosov and A. A. Zlotnik, “Generalized solutions ‘in the large’ of equations of one-dimensional motion of a viscous heat conducting gas,” Dokl. Akad. Nauk SSSR,301, No. 1, 11–15 (1988).
A. A. Zlotnik, “Estimates and stabilization of finite-difference equations of one-dimensional gravital magnetic gas dynamics,” Sov. J. Numer. Anal. Math. Model.,6, No. 4, 335–360 (1991).
Author information
Authors and Affiliations
Additional information
The work was supported by the Russian Foundation of Basic Research (Grant No. 93-011-1723).
Translated from Matematicheskie Zametki, Vol. 55, No. 5, pp. 51–68, May, 1994.
Rights and permissions
About this article
Cite this article
Zlotnik, A.A., Bao, N.Z. Properties and asymptotic behavior of solutions of some problems of one-dimensional motion of a viscous barotropic gas. Math Notes 55, 471–482 (1994). https://doi.org/10.1007/BF02110374
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02110374