Burgers PDE with piecewise constant initial condition

Question

Let's deal with this Burgers PDE:

You can see the characteristic curves below:

1. I believe the breaking time is $\boldsymbol{t_b=0}$, because it is the $\inf$ of $t$-coordinates of the intersection points of characteristics curves. Am I right?
2. How can I find the weak solution? How can I find the discontinuity line? At $t=0$ we have $x=\alpha$ and $x=\beta$ at the intersection points.

Thanks, in advance!