= Periodic backward-sawtooth Burgers solution
For the negative-flux equation $f_Z-ff_\theta=0$, a period-two increasing initial ramp develops rarefaction fans at odd points and steepens at even points. Before $Z=1$, its central ramp is $f=(\theta-2m)/(1-Z)$ on $|\theta-2m|<1-Z$, and its odd-point fans are $f=-(\theta-(2m+1))/Z$. After $Z=1$, stationary compressive shocks occupy the even points and $f=(2m+1-\theta)/Z$ between consecutive shocks. The amplitude decays as $1/Z$. The <Rankine-Hugoniot condition> and incoming <characteristic speeds> certify the post-breaking <entropy solution>.
Back to article page
