Higher-order asymptotic attraction of pullback attractors for a reaction–diffusion equation in non-cylindrical domains

In this paper, we consider the higher-order asymptotic attraction of pullback attractors for a reaction–diffusion equation with domains expanding in time. Firstly, to make the test functions meaningful, a maximum principle is proved for the corresponding variational solution; then, we establish some higher-order integrability results about the difference of variational solutions, and finally we prove the main result that the known (L2,L2)(L2,L2) pullback DλDλ-attractor can attract indeed the DλDλ class in LqLq-norm for any q∈[2,+∞)q∈[2,+∞).