4 problems

Let $K:(0,\infty)^2\to[0,\infty)$ be a coagulation kernel. It is $\gamma$-homogeneous when … for all $\lambda,x,y>0$, and gelation is the loss of mass from finite-mass particles th…

Scaling hypothesis. The behaviour of solutions $n$ to Smoluchowski's coagulation equation is self-similar as $t\to T_{*}$, perhaps under additional conditions on the initial datum.

Nonuniqueness conjecture. In this case, the uniqueness results for solutions in the infinite population regime will no longer hold.

Coagulation–transport conjecture. Coagulation overwhelms transport, so that the mass distribution densifies around large masses as $t\to\infty$.