Pullback attractors for the classical reaction-diffusion equation with time-dependent memory kernel
This paper presents a discussion on the long-time dynamical behavior of solutions for the classical reaction-diffusion equation with time-dependent memory kernel when nonlinear term adheres to subcritical growth and the external force term g(x,t)belongs to the space L2loc(R;L2(Ω))in the time-dependent space L2(Ω)×L2µt(R+;H10(Ω)).Within the new theorical framework,the well-posedness and the regularity of the solution,as well as the existence of the time-dependent pullback attractors are established.This is achieved by applying the delicate integral estimation method and decomposition techniques.
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