摘要：In this article, we consider the pullback attraction in $H_{0}^{1}$ of pullback attractor for semilinear heat equation with domains expanding in time. Firstly, we establish higher-order integrability of difference about variational solutions; then, we prove the continuity of variational solution in $H_{0}^{1}(O_{t})$. As application of continuity, we obtain the pullback $\mathscr{D}_{\lambda _{1}}$ attraction in $H_{0}^{1}$-norm..
