Upper semicontinuity of strong attractors for the Kirchhoff wave model with structural nonlinear damping. (21st January 2021)

• Record Type: Journal Article
• Authors: Qu, Yanxia; Yang, Zhijian
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 8(2021)
• Page Start: 6571
• Page End: 6580
• Publication Date: 2021-01-21
• Subjects: Kirchhoff wave model -- structural nonlinear damping -- strong global attractor -- upper semicontinuity of the attractors; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7209
• Languages: English
• ISSNs: 0170-4214

Abstract

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).