5 problems

Negative partial-sum conjecture. If there are pairwise different indices $i_1, \dots, i_{n-1}$ such that

Decay conjecture. In fact,

Universal-asymptotics conjecture. All solutions have this constructed asymptotic behaviour.

Global-attraction conjecture. In this parameter region, $(\bar p,\bar q,\bar r)$ is globally attracting.

Consider the two-dimensional parabolic-elliptic Patlak–Keller–Segel system … with nonnegative initial density $\rho_0$ and conserved mass … Here $\rho$ is the cell density,…