The inflow problem for the systems of equations of a viscous heat-conducting gas in the noncylindrical domains expanding in time

Abstract

For a complete system of equations of the one-dimensional nonstationary motion of some viscous heat-conducting gas, the global solvability is proved of the inflow problem in the noncylindrical domains expanding in time. The proof of the time-global existence and uniqueness theorem is connected with obtaining a priori estimates with the constants depending only on the data of the problem and the value of the time interval T but independent of the existence interval of the local solution.