Periodic solution and its stability of a damped BBM equation posed on $\mathbb{T}$

Abstract

In this paper, we are concerned with the existence and stability of temporal periodic solutions to a class of the Benjamin-Bona-Mahony (BBM) equation with damping in the torus $\mathbb{T}$, whose interior is applied with periodic force $f(x,t)$ with temporal period $\theta$. These types of solutions are established in $H^{\ell },\ell \ge 0$, and it is noteworthy to see that the I-energy method is invoked when low regularity of $\ell \in [0,1)$ is pursued.