GLOBAL REGULARITY FOR A NONLOCAL PDE DESCRIBING EVOLUTION OF POLYNOMIAL ROOTS UNDER DIFFERENTIATION
Publication
, Journal Article
Kiselev, A; Tan, C
Published in: SIAM Journal on Mathematical Analysis
January 1, 2022
In this paper, we analyze a nonlocal nonlinear partial differential equation formally derived by Steinerberger [Proc. Amer. Math. Soc., 147 (2019), pp. 4733-4744] to model dynamics of roots of polynomials under differentiation. This partial differential equation is critical and bears striking resemblance to hydrodynamic models used to describe collective behavior of agents (such as birds, fish, or robots) in mathematical biology. We consider a 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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Published In
SIAM Journal on Mathematical Analysis
DOI
EISSN
1095-7154
ISSN
0036-1410
Publication Date
January 1, 2022
Volume
54
Issue
3
Start / End Page
3161 / 3191
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
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Chicago
ICMJE
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Kiselev, A., & Tan, C. (2022). GLOBAL REGULARITY FOR A NONLOCAL PDE DESCRIBING EVOLUTION OF POLYNOMIAL ROOTS UNDER DIFFERENTIATION. SIAM Journal on Mathematical Analysis, 54(3), 3161–3191. https://doi.org/10.1137/21M1422859
Kiselev, A., and C. Tan. “GLOBAL REGULARITY FOR A NONLOCAL PDE DESCRIBING EVOLUTION OF POLYNOMIAL ROOTS UNDER DIFFERENTIATION.” SIAM Journal on Mathematical Analysis 54, no. 3 (January 1, 2022): 3161–91. https://doi.org/10.1137/21M1422859.
Kiselev A, Tan C. GLOBAL REGULARITY FOR A NONLOCAL PDE DESCRIBING EVOLUTION OF POLYNOMIAL ROOTS UNDER DIFFERENTIATION. SIAM Journal on Mathematical Analysis. 2022 Jan 1;54(3):3161–91.
Kiselev, A., and C. Tan. “GLOBAL REGULARITY FOR A NONLOCAL PDE DESCRIBING EVOLUTION OF POLYNOMIAL ROOTS UNDER DIFFERENTIATION.” SIAM Journal on Mathematical Analysis, vol. 54, no. 3, Jan. 2022, pp. 3161–91. Scopus, doi:10.1137/21M1422859.
Kiselev A, Tan C. GLOBAL REGULARITY FOR A NONLOCAL PDE DESCRIBING EVOLUTION OF POLYNOMIAL ROOTS UNDER DIFFERENTIATION. SIAM Journal on Mathematical Analysis. 2022 Jan 1;54(3):3161–3191.
Published In
SIAM Journal on Mathematical Analysis
DOI
EISSN
1095-7154
ISSN
0036-1410
Publication Date
January 1, 2022
Volume
54
Issue
3
Start / End Page
3161 / 3191
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics