steepens with time and characteristic curves can cross: multiple-valued solution?
- The viscous Burgers' equation (158)
is a parabolic PDE and has a unique solution for all times .
We look for a solution of the inviscid Burgers' equation that is a solution of
the viscous Burgers' equation in the limit
- Instead of a multiple-valued solution we get a discontinuity
where the characteristics end.
Discontinuities (shocks) are unavoidable
- Characteristics run into a shock from both sides.
- Discontinuities should be allowed in the initial conditions.
- We need to find weak solutions.