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.