A shock wave is a type of disturbance that moves through a medium at a speed greater than the speed of sound in that medium. This phenomenon is often characterized by a sudden and sharp change in pressure, temperature, and density, forming a steep front.
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A shock wave is a moving discontinuity of a weak solution to a conservation law. Its speed is fixed by the Rankine-Hugoniot condition, while an entropy condition selects the physically admissible direction of compression.