带非局部弱阻尼项的耦合吊桥方程的全局吸引子

Global attractors of coupled suspension bridge equations with nonlocal weak damping terms

摘要:

本文研究带有非局部弱阻尼项的耦合吊桥方程解的长时间动力学行为.本文首先利用单调算子理论建立了解的适定性,获得了解半群{S(t)}的耗散性,然后通过能量重建法验证了解半群{S(t)}的渐近光滑性,进而证明了带有非局部弱阻尼的耦合吊桥方程全局吸引子的存在性.

Abstract:

We investigate the long-time dynamical behavior of coupled suspension bridge equations with nonlocal weak damping terms. Firstly, we establish the well-posedness of the solutions based on the monotone operator theory. Secondly, the dissipation of solution semigroups {S(t)} is obtained. Then the asymptotic smoothness of solution semigroups {S(t)} is verified by using the energy reconstruction method. Fianlly the existence of global attractors for the coupled suspension bridge equations with nonlocal weak damping terms is proved.