In this paper we examine the history of the studying the dynamic compatibility conditions for gas-dynamic discontinuities, which determine the ratio between values of the gas-dynamic variables before the discontinuity and right behind him. The concepts of a shock wave, shock and the shock polar are introduced. The formation of ideas about the shock waves as a narrow region with abrupt changes in gas-dynamic parameters is shown with a staged scientific studies as an example. The relationship between the physical nature of gas-dynamic discontinuities and the appearance of singularities in solutions of the Euler equations for an ideal gas is shown. Burgers equation, which allows to simulate the shock waves is discussed. The article can serve as a brief introduction to the theory of gasdynamic discontinuities. It proposes the modern idea of gasdynamic discontinuities as the features arising in the solution of hyperbolic partial differential equations.
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