Abstract
The paper considers two-dimensional isentropic flows of polytropic gas, arising after the instantaneous destruction of the impermeable wall in the initial point in time separating a non-uniform resting gas from the vacuum. As a mathematical model, the system of equations of gas dynamics taking into account gravity is used. Using the initial data, the background flow and the sound characteristic propagating along it are built. In the system of equations of gas dynamics, a self-similar singularity is introduced into the independent variable $ x $ and the Cauchy problem with data on a sound characteristic is posed for the resulting system. From the necessary solvability conditions, the initial conditions are found. Next, the solution of the initial-boundary value problem is constructed in the form of a power series. The coefficients of the series are found when integrating ordinary differential equations.
Published Version
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