## Differential and Integral Equations

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

Thanh Nam Nguyen

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 14 June 2016

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