Abstract: When the nonlinear term satisfied the subcritical growth condition, long-time dynamical behavior of solutions for nonlocal nonclassical diffusion equation with time-dependent memory kernels was discussed. We first used  Galerkin approximation method to obtain the well-posedness and regularity of the solution, and then used decomposition technique and integral estimation method to prove the existence and regularity of the time-dependent global attractors.

Key words: nonlocal , nonclassical diffusion equation,  , time-dependent memory kernel, time-dependent global attractor, regularity