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$$

\frac{\partial\rho}{\partial t} + 2\rho\frac{\partial\rho}{\partial x} = 0

$$

with the piecewise constant initial conditions

$$

\rho(x,0) = \begin{cases}

\rho_1, & x < -x_0\\

\rho_2, & -x_0 < x < x_0\\

\rho_3, & x > x_0

\end{cases}

$$

where $\rho_1 > \rho_2 > \rho_3$ and $\rho_i, x_0\in\mathbb{R}$ with $i = 1, 2, 3$.

Argue that two shocks form at $x = \pm x_0$ in this case and sketch the space-time diagram for the density field.

I have no idea on what to do or how to start.