Strong Attractors for the Structurally Damped Kirchhoff Wave Models with Subcritical-Critical Nonlinearities

Strong attractors and their stability for the structurally damped Kirchhoff wave equation with supercritical nonlinearity

“…From then on, there have been many researches on the well-posedness and asymptotic behavior of the Kirchhoff type wave models with fractional dissipations: (−Δ) 𝛼 u t , with 0 ≤ 𝛼 ≤ 1 or nonlinear dissipation h(u t ), with h(s)s ≥ 0, s ∈ R (see, e.g. [17][18][19][20][21][22][23][24][25][26][27][28] and references therein).…”

“…From then on, there have been many researches on the well‐posedness and asymptotic behavior of the Kirchhoff type wave models with fractional dissipations: $$$ {\left(-\Delta \right)}^{\alpha }{u}_t $$$, with $$$ 0\le \alpha \le 1 $$$ or nonlinear dissipation $$$ h\left({u}_t\right) $$$, with $$$ h(s)s\ge 0,s\in \mathrm{\mathbb{R}} $$$ (see, e.g. [17–28] and references therein).…”