论文标题
有界域中弱阻尼的五重拳方程的强吸引子
Strong attractors for weakly damped quintic wave equation in bounded domains
论文作者
论文摘要
在本文中，我们根据$ \ mathbb {r}^3的有界平滑域中的五峰非线性的弱阻尼波方程的长期动力学研究3. $基于对有限域的情况的估计，我们在相位空间$ h^2（pap h^2（ω）\ pap h^1_0（ω）中，我们确定了强大的全球吸引者的存在h^1_0（ω）$。此外，在准稳定估计的帮助下，还显示了吸引子的有限分形维。
In this paper, we study the longtime dynamics for the weakly damped wave equation with quintic non-linearity in a bounded smooth domain of $\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded domains, we establish the existence of a strong global attractor in the phase space $H^2(Ω)\cap H^1_0(Ω)\times H^1_0(Ω)$. Moreover, the finite fractal dimension of the attractor is also shown with the help of the quasi-stable estimation.
