A class of solutions of the gas-dynamics equations containing a function ar
bitrariness is used for a qualitative and quantitative analysis of the gas
flow which occurs as a result of the interaction between Riemann compressio
n waves. Two types of flow are investigated matched flow, when the adiabati
c exponent is matched in a special way with the initial geometry of the com
pressed volume, and the general case when there is no such matching. For ma
tched interaction of non-self-similar Riemann waves, a phenomenon of partia
l collapse is established (only part of the initial mass of the gas is comp
ressed to a point); here the asymptotic estimates for the velocity, density
, internal energy and optical thickness are the same as for self-similar co
mpression. It is proved that unmatched interaction of self-similar Riemann
waves does not lead to unlimited unshocked compression of the gas; in this
case a shock wave occurs when the maximum density of the gas is finite. The
results obtained enable us to say that two-dimensional processes of unlimi
ted compression are stable for a fairly wide range of perturbations. (C) 19
99 Elsevier Science Ltd. All rights reserved.