论文标题
在3-D域中具有非局部弱阻尼和SUP-ALINERITY的波动方程的长期动力学
Long-time dynamics of the wave equation with nonlocal weak damping and sup-cubic nonlinearity in 3-D domains
论文作者
论文摘要
在本文中，我们研究了在$ \ mathbb {r}^3的有限平滑域中，具有非局部弱阻尼和SUP-Allinearity的波动方程的长期动力学。$基于有界域的strichartz估计值，我们首先证明了Shatah-Struwe seluwe shatah-struwe selutions shatah-struwe selutions的全球范围。然后，我们通过承包功能的方法建立了Shatah-Struwe解决方案Semigroup的全球吸引子的存在。最后，我们验证了该半群的多项式吸引子的存在。
In this paper, we study the long-time dynamics for the wave equation with nonlocal weak damping and sup-cubic nonlinearity in a bounded smooth domain of $\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded domains, we first prove the global well-posedness of the Shatah-Struwe solutions. Then we establish the existence of the global attractor for the Shatah-Struwe solution semigroup by the method of contractive function. Finally, we verify the existence of a polynomial attractor for this semigroup.
