Smooth regions with
Lax entropy condition:
For a convex scalar conservation law, a discontinuity
propagating with speed
satisfies the Lax entropy condition if
- What about steps with
- Expansion shock with characteristics running out of it is weak solution.
- But: any small but non-zero viscosity would smooth the step and cause a rarefaction wave
(or rarefaction fan).
- Only solutions that fulfil an
- Therefore: expansion shocks are not allowed.
- An entropy condition destroys time-reversibility.