Geodesic
An ingression problem for the systems of equations of a~viscous heat-conducting gas in time-increasing noncylindrical domains
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 1, pp. 28-44

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The global solvability of an ingression problem for the complete system of equations describing one-dimensional nonstationary flow of a viscous heat-conducting gas in time-increasing noncylindrical domains is proved. The proof of the existence and uniqueness theorem of the total solution with respect to time is connected with obtaining a priori estimates in which the constants depend only on the data of the problem and the length of the time interval $T$ but do not depend on the existence interval of a local solution.
Keywords: system of the Navier–Stokes equations, heat-conducting gas, global solvability, time-increasing non-cylindrical domains. 
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     author = {I. A. Kaliev and A. A. Shukhardin and G. S. Sabitova},
     title = {An ingression problem for the systems of equations of a~viscous heat-conducting gas in time-increasing noncylindrical domains},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {28--44},
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     volume = {18},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2015_18_1_a2/}
}
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I. A. Kaliev; A. A. Shukhardin; G. S. Sabitova. An ingression problem for the systems of equations of a~viscous heat-conducting gas in time-increasing noncylindrical domains. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 1, pp. 28-44. http://geodesic.mathdoc.fr/item/SJIM_2015_18_1_a2/