Upper semicontinuity of strong attractors for the Kirchhoff wave model with structural nonlinear damping

In this paper, we prove the upper semicontinuity of the strong global attractors θon 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 ) θu 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 θon 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).