September/October 2016 On the $\omega$-limit set of a nonlocal differential equation: Application of rearrangement theory
Thanh Nam Nguyen
Differential Integral Equations 29(9/10): 939-956 (September/October 2016). DOI: 10.57262/die/1465912611

Abstract

We study the $\omega$-limit set of solutions of a nonlocal ordinary differential equation, where the nonlocal term is such that the space integral of the solution is conserved in time. Using the monotone rearrangement theory, we show that the rearranged equation in one space dimension is the same as the original equation in higher space dimensions. In many cases, this property allows us to characterize the $\omega$-limit set for the nonlocal differential equation. More precisely, we prove that the $\omega$-limit set only contains one element.

Citation

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Thanh Nam Nguyen. "On the $\omega$-limit set of a nonlocal differential equation: Application of rearrangement theory." Differential Integral Equations 29 (9/10) 939 - 956, September/October 2016. https://doi.org/10.57262/die/1465912611

Information

Published: September/October 2016
First available in Project Euclid: 14 June 2016

zbMATH: 1374.35067
MathSciNet: MR3513588
Digital Object Identifier: 10.57262/die/1465912611

Subjects:
Primary: 35B40 , 35R09 , 45K05

Rights: Copyright © 2016 Khayyam Publishing, Inc.

Vol.29 • No. 9/10 • September/October 2016
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