4 problems

Let $u$ and $v$ be solutions for which the relative mass is conserved, meaning that the integral of their difference is invariant in time. For $p>1$, consider the corresponding rel…

Consider the coagulation-fragmentation system with density $\rho(s,t)$, coagulation operator $Q_C$, fragmentation operator $Q_F$, and kernels … for $s,\hat s>0$. Let … be the $k$-t…

Let $K:(0,\b7infty)\times(0,\infty)\to[0,\infty)$ be a coagulation kernel and let $\kappa>0$. A kernel is called non-gelling if all solutions conserve mass, and gelling if mass con…

Mass-conservation conjecture. Conservation of mass should hold: for every solution with initial datum $u_0$, one has