---
tag: JSDMGGTG7G
kind: concept
name: Shock wave
msc: [35L67, 35L65, 76L05]
sources:
  - url: https://en.wikipedia.org/wiki/Shock_wave
---

## Summary

In the theory of [[conservation laws|8RA7AMWSAF]], a shock wave is a jump discontinuity of a weak solution that moves along a curve in spacetime.
Its speed is fixed by the [[Rankine–Hugoniot conditions|S4XMYJ3V42]], and an entropy condition decides which jumps are physically admissible.
Shocks form in finite time from smooth data in nonlinear equations such as [[Burgers' equation|NEGHXN8RE1]], so they are unavoidable in the theory.
They model the sudden jumps of pressure and density in gas dynamics, such as the shock in front of a supersonic aircraft.
See the [[definition|A5GDAAYNM0]].

## Explanations

### L1 human

On a road, fast cars catch up with slow cars ahead of them, and a sharp edge of a traffic jam forms.
Behind the edge the traffic is dense, in front of it the road is nearly free, and the edge itself moves.
This moving jump is a shock wave.
For Burgers' equation with value $1$ on the left and $0$ on the right, the jump moves to the right at speed $1/2$, the average of the two values.