摘要：In non-cylindrical domains, we use the definition of the variational solution and the maximum principle (the Galerkin method used usually in a cylindrical domain cannot be applied directly) to prove the existence of a pullback D λ 1 $\mathscr {D}_{\lambda_)}$ attractor in L p ( O t ) $L^{p}(\mathcal{O}_{t})$ (any p ⩾ 2 $p\geqslant 2$ ) for a reaction-diffusion equation. Then, with an appropriate assumption, the higher-order integrability of variational solution is obtained. Finally, we discuss the existence of a pullback D λ 1 $\mathscr{D}_{\lambda_)}$ attractor in L 2 + δ ( O t ) $L^{2+\delta}(\mathcal{O}_{t})$ for any δ ∈ [ 0 , + ∞ ) $\delta\in[0,+\infty)$ .
