论文标题
弱潮湿的kawahara方程式的全球吸引子
Global attractor for the weakly damped forced Kawahara equation on the torus
论文作者
论文摘要
我们研究了在圆环上弱阻尼强迫的卡瓦哈拉方程的解决方案的长时间行为。更确切地说，我们证明了$ l^2 $中的全球吸引子的存在，随着时间的流逝，所有解决方案都会更加接近。实际上，我们表明，全球吸引子恰好在一个平滑的空间中$ h^2 $，并在其中进行了界定。此外，我们在$ h^2 $中给出吸引子大小的上限，这仅取决于阻尼参数和强迫术语的规范。
We study the long time behaviour of solutions for the weakly damped forced Kawahara equation on the torus. More precisely, we prove the existence of a global attractor in $L^2$, to which as time passes all solutions draw closer. In fact, we show that the global attractor turns out to lie in a smoother space $H^2$ and be bounded therein. Further, we give an upper bound of the size of the attractor in $H^2$ that depends only on the damping parameter and the norm of the forcing term.
