Differential and Integral Equations

On the $\omega$-limit set of a nonlocal differential equation: Application of rearrangement theory

Thanh Nam Nguyen

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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.

Article information

Differential Integral Equations, Volume 29, Number 9/10 (2016), 939-956.

First available in Project Euclid: 14 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B40: Asymptotic behavior of solutions 35R09: Integro-partial differential equations [See also 45Kxx] 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]


Nguyen, Thanh Nam. On the $\omega$-limit set of a nonlocal differential equation: Application of rearrangement theory. Differential Integral Equations 29 (2016), no. 9/10, 939--956. https://projecteuclid.org/euclid.die/1465912611

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