Abstract
The solutions of initial-boundary-value problems describing the shockless compression of cylindrically and spherically symmetric layers on an ideal polytropic gas to infinite density are investigated. Attention is also devoted to the quasi-one-dimensional case, when the surface on which the compression takes place is in one-to-one correspondence with the sonic characteristic surface separating the initial background flow and the compression wave. The solutions are expanded in convergent power series in a space of special dependent and independent variables, both in the neighbourhood of the final time. Asymptotic laws of shockless strong compression are found, and it is proved that they are described by curves in the convergence domains of the series. The additional external energy resources required for the transition from the compression of plane layers to that of quasi-one-dimensional layers are shown to be finite, provided that the polytropy index of the gas is not greater than three.
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