= Solution
The initial condition is a period-one square wave: height one on each interval $[k-1/2,k]$ and zero on each gap $(k,k+1/2)$, for integer $k$. Each period has mean $1/2$.
\Image[/past-exam-of-the-applied-partial-differential-equations-course-of-the-university-of-oxford/2023-periodic-burgers-evolution.png]
{title=A periodic train of pulses evolves into a travelling sawtooth of decreasing amplitude}
{description=Original exact profiles at $t=0$, $t=0.5$, $t=1$, and $t=3$. The dashed line marks the conserved mean $1/2$. Jump-point values can be chosen without changing the weak solution.}
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