AI 中文总结
研究环面\(\mathbb{T}\)上带阻尼BBM方程周期解的存在性与稳定性，通过I-能量方法在\(H^{\ell}, \ell\geq 0\)中建立解，尤其在\(\ell\in[0, 1)\)低正则性时使用该方法。
AI 中文摘要
本文研究环面\(\mathbb{T}\)上一类带阻尼的Benjamin-Bona-Mahony（BBM）方程时间周期解的存在性与稳定性，其内部施加有时间周期为\(\theta\)的周期力\(f(x, t)\)。这些解在\(H^{\ell}, \ell\geq 0\)中建立，值得注意的是，当\(\ell\in[0, 1)\)的正则性较低时调用了I-能量方法。
英文摘要
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 $θ$. 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.
