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Upper semicontinuity of strong attractors for the Kirchhoff wave model with structural nonlinear damping
Author(s) -
Qu Yanxia,
Yang Zhijian
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7209
Subject(s) - attractor , dissipative system , mathematics , nonlinear system , space (punctuation) , mathematical analysis , topology (electrical circuits) , continuation , physics , computer science , combinatorics , quantum mechanics , programming language , operating system
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).