Geodesic
Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases
Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 835-846.

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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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     title = {Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases},
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A. A. Zlotnik; A. A. Amosov. Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases. Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 835-846. http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a3/

[1] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1978 | Zbl

[2] Antontsev S. N., Kazhikhov A. V., Monakhov V. N., Kraevye zadachi mekhaniki neodnorodnykh zhidkostei, Nauka, Novosibirsk, 1983 | Zbl

[3] Amosov A. A., “Korrektnost “v tselom” nachalno-kraevykh zadach dlya sistemy uravnenii dinamiki vyazkogo izluchayuschego gaza”, Dokl. AN SSSR, 280:6 (1985), 1326–1329 | MR | Zbl

[4] Amosov A. A., Zlotnik A. A., “A study of a finite-difference method for the one-dimensional viscous heat conductive gas flow equation. I: A priori estimates and stability”, Sov. J. Numer. Anal. and Math. Model., 2:3 (1987), 159–178 | MR | Zbl

[5] Amosov A. A., Zlotnik A. A., “Raznostnaya skhema na neravnomernoi setke dlya uravnenii odnomernoi magnitnoi gazovoi dinamiki”, ZhVMiMF, 29:4 (1989), 521–534 | MR | Zbl

[6] Amosov A. A., Zlotnik A. A., “Obobschennye resheniya “v tselom” uravnenii odnomernogo dvizheniya vyazkogo teploprovodnogo gaza”, Dokl. AN SSSR, 301:1 (1988), 11–15 | Zbl

[7] Amosov A. A., Zlotnik A. A., “Razreshimost “v tselom” sistemy uravnenii odnomernogo dvizheniya neodnorodnogo vyazkogo teploprovodnogo gaza”, Matem. zametki, 52:2 (1992), 3–16 | MR | Zbl

[8] Padula M., “Existence and continuous dependence for solutions to the equations of a one-dimensional model in gas-dynamics”, Meccanica, 16 (1981), 128–135 | DOI | Zbl

[9] Amosov A. A., Zlotnik A. A., “Edinstvennost i ustoichivost obobschennykh reshenii odnogo klassa kvazilineinykh sistem uravnenii sostavnogo tipa”, Matem. zametki, 55:6 (1994), 13–31 | MR | Zbl

[10] Amosov A. A., Zlotnik A. A., “Razreshimost “v tselom” odnogo klassa kvazilineinykh sistem uravnenii sostavnogo tipa s negladkimi dannymi”, Differents. uravneniya, 30:4 (1994), 596–609 | MR | Zbl