So here is the problem statement:
In addition, the following "hint" is given:Consider the equation
Let be a solution of (6.12) in each of two regions separated by a curve . Let be continuous, but have a jump discontinuity along the curve. Prove that
and hence that the curve is characteristic.
I believe denote the limits of from the right and left, respectively, and similarly for .Hint: By (6.12)
Moreover, and are continuous on the curve.
This is all from Fritz John's Partial Differential Equations, exercise 1.6.3, p19.
I'm pretty lost on this one. Any help would be much appreciated. Thanks !