We investigate global thermal overstability in the postshock gas Ñow behind radiative shock waves and its possible role in the fragmentation of shock-compressed gas, by linear perturbation analysis. In order to examine whether the thermal overstability can introduce any characteristic scale length into the fragmentation, we explore the existence of the maximum growth mode with a Ðnite wavelength. We take into account antisymmetric modes of perturbation, as well as symmetric ones, and a cold

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... r with Ðnite thickness, and we examine a wide range of parameters. The new results of this paper are : (1) there are two kinds of modes, overstable and quasi-oscillatory ; (2) unlike previous results, we do not Ðnd a dominance of low-order modes over high-overtone ones. We Ðnd a scaling relation in dispersion relations of overstable modes, which means that there is no maximum growth mode. We show that the Ðnite thickness of the cold layer only helps make clearer the di †erence between overstable and quasioscillatory modes compared to the zero cold layer thickness cases. We conclude that at least within the linear analysis, the global thermal overstability does not introduce speciÐc length scales to the fragmentation. We present a schematic picture of the driving mechanism of the global thermal instability behind radiative shock waves, and elucidate the di †erence between the stability properties of radiative and wellstudied isothermal shock waves.