https://neckpinch.com/authors/michael-rozowski/New arXiv papers by Michael Rozowski, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2408.14309/arxiv:2408.14309Mon, 26 Aug 2024 00:00:00 GMTAntoine Mellet, Michael Rozowski — The Patlak-Keller-Segel system of equations (PKS) is a classical example of aggregation-diffusion equation in which the repulsive effect of diffusion is in competition with the attractive chemotaxis term. Recent work on the Parabolic-Elliptic PKS model have shown that when the repulsion is modeled by a nonlinear diffusion term ρ∇ρ^(m-1) with m>2, this competition leads to phase separation phenomena. Furthermore, in some asymptotic regime corresponding to a large population observed over a long enough time, the interface separating regions of high and low density evolves according to the Hele-Shaw free boundary problem with surface tension. In the present paper, we consider the counterpart of that model, namely the Elliptic-Parabolic PKS model and we prove that the same phase separation phenomena occurs, but the motion of the interface is now described (asymptotically) by a volume-preserving mean-curvature flow.Mean curvature flowVolume-preserving & constrained flowsFree boundary & capillary