An ingression problem for the systems of equations of a viscous heat-conducting gas in time-increasing noncylindrical domains

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.