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Wednesday, 19 May 2021 01:41

Global regularity for a nonlocal PDE describing evolution of polynomial roots under differentiation

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Alexander Kiselev, and Changhui Tan


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.


 This work is supported by NSF grant DMS #1853001 and DMS #2108264

This paper is the first part of the preprint arXiv:2012.09080.

Read 61 times Last modified on Monday, 19 July 2021 01:44