Alexander Kiselev, and Changhui Tan
SIAM Journal on Mathematical Analysis, Volume 54, No. 3, pp. 3161-3191 (2022).
Abstract
In this paper, we analyze a nonlocal nonlinear partial differential equation formally derived by Stefan Steinerberger to model dynamics of roots of polynomials under differentiation. This partial differential equation is critical and bears striking resemblance to hydrodynamic models used to described collective behavior of agents (such as birds, fish or robots) in mathematical biology. We consider periodic setting and show global regularity and exponential in time convergence to uniform density for solutions corresponding to strictly positive smooth initial data.
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doi:10.1137/21M1422859 |
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This work is supported by NSF grant DMS #1853001 and DMS #2108264 |