Based on the Fourier law of heat conduction, this paper was concerned with the thermoelastic Timoshenko system with memory and variable delay in the internal feedback, which describes the transverse vibration of a beam. By the Lummer-Phillips theorem and the variable norm technique suitable for the nonautonomous operator, the stability of the coupled system has been derived in space $\mathcal{H}$.

We study the Benjamin-Bona-Mahony model with finite distributed delay in 3D, which depicts the dispersive impact of long waves. Based on the well-posedness of model, the family of pullback attractors for the evolutionary processes generated by a global weak solution has been obtained, which is unique and minimal, via verifying asymptotic compactness in functional space with delay $C_V$ and topological space $V\times C_V$, where the energy equation method and a retarded Gronwall inequality are utilized.