ИСТИНА

We demonstrate possibilities of time rescaling on example of barotropic gas dynamics (GD) system, corresponding to conservation of mass, momentum and energy. The system consists of three equations for density, velocity and pressure. We show that for small time GD equations can be reduced to nonlinear heat equation, for large time - to pressureless gas dynamics, and for intermediary time - to pressureless gas dynamics equations with friction term. Also we show that the approach of singular perturbation can help to find the small time asymptotics of the Cauchy problem for GD in terms of the nonlinear heat equation.