1. Strong Attractors for the Structurally Damped Kirchhoff Wave Models with Subcritical-Critical Nonlinearities.
- Author
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Da, Fang, Yang, Zhijian, and Sun, Yue
- Subjects
- *
HOLDER spaces , *WAVE equation , *CONTINUITY - Abstract
The paper investigates the well-posedness and the regularity of the solutions, the existence and the continuity of the strong attractors for the structurally damped Kirchhoff wave models with subcritical-critical nonlinearities: u tt - (1 + ϵ ‖ ∇ u ‖ 2 ) Δ u + (- Δ) α u t + h (u t) + g (u) = f (x) , where ϵ ∈ [ 0 , 1 ] is a perturbed extensibility parameter, α ∈ [ 1 / 2 , 1) is a dissipative index. We show that when the nonlinearity g(u) is of either critical growth as α ∈ (1 / 2 , 1) or subcritical growth as α = 1 / 2 , while h (u t) is of critical growth depending on α , the model is well-posed and its weak solution is exactly the strong one; the related solution semigroup S ϵ (t) has a strong (X, Y)-global attractor and a strong (X, Y)-exponential attractor, which are also the standard global and exponential attractor of optimal regularity of S ϵ (t) in X, respectively, where X is the energy space and Y is the strong solution space; these global attractors are upper semicontinuous and these exponential attractors are Hölder continuous with respect to perturbed parameter ϵ in the sense of Y-topology, respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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