Localized compression regimes in a heat-conducting gas

The effect of limiting regimes with peaking on a compressible sphere with thermal conductivity $\varkappa=\varkappa_0\rho^\alpha T^\beta$, $\beta>0$, is examined. The investigation is carried out for selfsimilar solutions of the power type. Conditions are established for shockless supercompression of the material and joint localization of the thermal and gas-dynamic processes, which depend on the thermophysical properties of the medium and the limiting law. The phenomena are also investigated numerically.