Acta Mathematica Vietnamica

We study the asymptotic behavior of solutions to a class of retarded non-autonomous semilinear parabolic equations with nonlinearities of polynomial type, general delays and time-dependent external forces. The existence of weak solutions for the equations is proved by using the Galerkin method. We then prove the existence of a pullback attractor without restriction on the growth order of polynomial type nonlinearity and on exponential growth of the external force. When the time-dependent external force is a translation bounded function, the existence of a uniform attractor is proved. Finally, we give a relationship between the pullback attractor and the uniform attractor.

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