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. 
@article{MZM_1998_63_6_a3,
     author = {A. A. Zlotnik and A. A. Amosov},
     title = {Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases},
     journal = {Matemati\v{c}eskie zametki},
     pages = {835--846},
     publisher = {mathdoc},
     volume = {63},
     number = {6},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a3/}
}
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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/