衰退记忆型无阻尼吊桥方程的时间依赖拉回吸引子

Time-Dependent Pullback Attractors for Non-damping Suspension Bridge Equation with Fading Memory

基于时间依赖空间上的过程理论,考虑带有衰退记忆的无阻尼吊桥方程解的长时间动力学行为.首先,利用Faedo-Galerkin逼近法得到解的适定性;其次,利用能量估计得到该非自治动力系统在相应解空间中存在拉回吸收集;最后,利用收缩函数方法和共圈技术证明时间依赖拉回吸引子的存在性.

Based on the process theory in time-dependent space,we considered the long-time dynamic behavior of the solution for the non-damping suspension bridge equation with fading memory.Firstly,we obtained well-posedness of solution by using Faedo-Galerkin approximation method.Secondly,the non-autonomous dynamical system had pullback absorb set in the corresponding solution space was obtained by using energy estimation.Finally,we proved the existence of time-dependent pullback attractors by using the contraction function method and cocyclic technique.