Burgers Equation — Shock Formation

The inviscid Burgers equation ∂u/∂t + u∂u/∂x = 0 forms shocks from smooth initial data. Add viscosity to regularize. Watch characteristics cross and shocks emerge.

Parameters

∂u/∂t + u∂u/∂x = ν∂²u/∂x²
Characteristics: dx/dt = u
Shock: t* = -1/min(du/dx)₀

Viscosity ν0.001 Speed1.0

t = 0.000
ν = 0.001
Max |u| = 0.000