Upper semicontinuity of strong attractors for the Kirchhoff wave model with structural nonlinear damping. (21st January 2021) - Qu, Yanxia; Yang, Zhijian
Abstract : In this paper, we prove the upper semicontinuity of the strong global attractors 𝒜 θ on the dissipative index θ in the topology of the stronger space for the Kirchhoff wave model with structural nonlinear damping: u t t − ϕ ( ‖ ∇ u ‖ 2 ) △ u + σ ( ‖ ∇ u ‖ 2 ) ( − Δ ) θ u t + f ( u ) = g ( x ), with θ  ∈ [1/2,  1). It is continuation of the research in recent literatures 1, 2 where the upper semicontinuity of the strong attractor 𝒜 θ on θ in the topology of natural energy space is obtained. This result improves and deepens those in recent literatures (Li and Yang in J Differ Equat. 2020; 268: 7741‐7743; Li, Yang and Ding in Appl. Math. Lett. 2020; 104:106258).