u(x,t) — Burgers eq.
Method of Characteristics
Spacetime (x-t) diagram
Viscous vs Inviscid shock

Shock Formation

Burgers: ∂u/∂t + u·∂u/∂x = ν∂²u/∂x²
Inviscid: ∂u/∂t + u·∂u/∂x = 0
Shock time: t* = 1/max(-u'₀(x))
Rankine-Hugoniot: s = (u₊+u₋)/2