We model the hydrodynamic interaction of a shock wave of an evolved supernova remnant with a small interstellar gas cloud like the ones observed in the Cygnus loop and in the Vela SNR. We investigate the interplay between radiative cooling and thermal conduction during cloud evolution and their effect on the mass and energy exchange between the cloud and the surrounding medium. Through the study of two cases characterized by different Mach numbers of the primary shock (M = 30 and 50, corresponding to a post-shock temperature $Tapprox 1.7times 10^6$ K and $approx 4.7times 10^6$ K, respectively), we explore two very different physical regimes: for M = 30, the radiative losses dominate the evolution of the shocked cloud which fragments into cold, dense, and compact filaments surrounded by a hot corona which is ablated by the thermal conduction; instead, for M = 50, the thermal conduction dominates the evolution of the shocked cloud, which evaporates in a few dynamical time-scales. In both cases we find that the thermal conduction is very effective in suppressing the hydrodynamic instabilities that would develop at the cloud boundaries.
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