arXiv subjects

Thanh Nam Nguyen

Publications and source records attributed to Thanh Nam Nguyen.

2 recordsLinked to original sources

arXiv2016

On the $ω$-limit set of a nonlocal differential equation: application of rearrangement theory

We study the $ω$-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 $ω$-limit set for the nonlocal differential equation. More precisely, we prove that the $ω$-limit set only contains one element.

math.AP↗

arXiv2015

On the large time behavior of the solutions of a nonlocal ordinary differential equation with mass conservation

We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal term is expressed in terms of spatial integration. We discuss the large time behavior of solutions and prove, among other things, the convergence to steady-states. The proof that the solution orbits are relatively compact is based upon the rearrangement theory.

math.AP↗