4 problems

Let $(\rho_t)_{t\geq 0}$ be the curve of marginal laws associated with the controlled swarm gradient dynamics, and let $\rho_\infty$ denote its limiting measure. Let $\beta(t)$ be…

Let $\mu_t^\infty$ be a solution of the limiting dynamics whose initial condition is a finite mixture of spherical heat kernels, and suppose that one component collapses to a Dirac…

Descent conjecture. An analogous descent property should hold for $\widehat{F}$: along solutions $p(\cdot)$ of the limiting equation, $\frac{d}{dt}\widehat{F}(p(t))\leq 0$, with eq…

The one-population BCC equations are considered with an activation function that is positive, meaning non-negative-valued as specified in the source. An oscillatory solution is cal…