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This study solves the initial and boundary value problem for the Euler equations of gases. The boundaries are allowed to move and are assumed to be adiabatic. In addition we shall discuss that isothermal walls are not possible within the Euler theory. We do not formulate the boundary conditions in terms of the macroscopic basic variables mass density, velocity and temperature. Instead we consider the underlying kinetic picture which exhibits the interaction of the gas atoms with the boundaries. Hereby the advantage is offered to formulate the boundary conditions in a very suggestive manner. This procedure becomes possible, because we approach the solution of the Euler equations by the following limit: We rely on the moment representation of the macroscopic basic variables, and in order to obtain the temporal development of the phase density, we decompose a given macroscopic time interval into periods of free flight of the gas atoms. These periods of duration TME are interrupted by a maximization of entropy, thus introducing a simulation of the interatomic interaction. In [2] we have shown that the Euler equations may be established in the limit TME → 0.