Continuity And Dynamics Of A Non-autonomous Reaction-diffusion Equation

We prove some higher-order integra.bility near the initial time for the solution of a non-autonomous reaction-diffusion equationAs the applications of this result, we first prove the continuity of solutions in H01(Ω) with respect to initial data, then we prove that the attraction in the usual (L2, L2)(?)-pullback attractor indeed can be L22+δ-norm for any δ∈[0,∞), and give a very simple proof about the existence of pullback attractor in H01(Ω).