Stability of adiabatic compression of ideal gas by thin shell

The complete solution of hydrodynamic problem of the centered isentropic compression wave in an ideal gas is constructed. The problem is formulated in Lagrange variables. The gas is assumed to be initially motionless with uniform density and pressure. The problem is solved in plane, cylindrical and spherical cases in the unified manner. In the second part stability problem of thin massive shell is considered. Equations that describe evolution of small perturbations of thin massive shell in the case when its acceleration depended on time are derived. The shell is assumed to be structureless; the mass of the shell is supposed to be much more than the mass of the gas surrounding the shell. This problem is solved in plane, cylindrical, and spherical geometry. Finally we examine the stability problem of the shell providing the isentropic compression of the gas. The stability is considered with respect to small perturbations in the form of angular harmonics and plane waves. Increments of amplitude growth are calculated for both types of perturbations. The study reveals that the growth of the plane wave type perturbations is limited and that the one of the angular harmonic type is unlimited.