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Dissipation for a non-convex gradient flow problem of a Patlack-Keller-Segel type for densities on $\mathbb{R}^n$, $n\geq 3$. (arXiv:1712.04885v1 [math.AP])
来源于:arXiv
We study an evolution equation that is the gradient flow in the
$2$-Wasserstien metric of a non-convex functional for densities in
$\mathbb{R}^n$ with $n \geq 3$. Like the Patlack-Keller-Segel system on
$\mathbb{R}^2$, this evolution equation features a competition between the
dispersive effects of diffusion, and the accretive effects of a concentrating
drift. We determine a parameter range in which the diffusion dominates, and all
mass leaves any fixed compact subset of $\mathbb{R}^n$ at an explicit
polynomial rate. 查看全文>>
