带时滞项的Boussinesq-Beam方程的拉回吸引子

利用压缩函数的方法和相关理论，研究带时滞项的Boussinesq-Beam方程的拉回吸引子的存在性:首先通过作内积和不等式估计得到拉回吸收集的存在性，然后借助构造具体的能量泛函并结合收缩函数法的思想验证带时滞项的Boussinesq-Beam方程的解所生成的过程$ \{U(t, \tau)\}_{t \geqslant \tau}$在$ C_{D(A), V}$中是渐近紧的，最后证明过程$ \{U(t, \tau)\}_{t \geqslant \tau}$在$ C_{D(A), V}$中存在拉回吸引子.

Pullback Attractors for the Boussinesq-Beam Equation with Time Delay

The existence of pullback attractors for the Boussinesq-Beam equation with time delay is handled with the concept of contractive function and some related method. Firstly, the existence of a pullback absorbing set is verified by taking the inner product and estimating the inequalities. Then the specific energy function is constructed and the method of contractive functions is used to prove that the process $ \{U(t, \tau)\}_{t \geqslant \tau}$ in $ C_{D(A), V}$ produced by the Boussinesq-Beam equation with time delay possess compactness. Finally, the existence of pullback attractors in $ C_{D(A), V}$ for the process $ \{U(t, \tau)\}_{t \geqslant \tau}$ is proved.