Uniform attractors for non-autonomous parabolic equations with delays

Abstract

The present paper is devoted to the asymptotic behavior of non-autonomous parabolic equations with nonlinearity containing general delay and with time-dependent external forces. The existence, uniqueness and regularity of solutions for the equation are obtained. If the time-dependent external forces is a translation compact function in L loc 2 ( R , L 2 ( Ω ) ) , then, the existences of uniform attractor for non-autonomous dynamics system are provided, and the structures of attractors are also studied, which is the union of all bounded complete trajectory of the equation at a time moment. Finally, the main results are applied to the population dynamics with distributed state-dependent delay and with almost periodic external force, and the uniform attractor and its kernel section are obtained.