Higher-order asymptotic attraction of pullback attractors for a reaction–diffusion equation in non-cylindrical domains. (January 2015) - Xiao, Yanping; Sun, Chunyou
Abstract: 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 ( L 2, L 2 ) pullback D λ -attractor can attract indeed the D λ class in L q -norm for any q ∈ [ 2, + ∞ ) .