In this paper, we are interested in the long-time behavior of solutions to a nonlocal interaction equation in dimension $1$. We show that, up to an extraction, the solution converges to a steady-state. Then, we study the structure of stable steady-states.
Gaël Raoul. "Nonlocal interaction equations: Stationary states and stability analysis." Differential Integral Equations 25 (5/6) 417 - 440, May/June 2012. https://doi.org/10.57262/die/1356012673