2 problems

Rarefaction stability conjecture. The long-time behavior of solutions is governed by the smoothed Riemann solution of the corresponding inviscid system.

Consider the cubic Burgers equation with flux $f(u)=u^3$ and Riemann initial data $u_-$ and $u_+$. If $u_-<0$ and … or if $u_->0$ and … then the inviscid Riemann solution consists…