Pullback Attractors for Nonautonomous Degenerate Kirchhoff Equations with Strong Damping

Abstract

In this paper, we obtain the existence of pullback attractors for nonautonomous Kirchhoff equations with strong damping, which covers the case of possible generation of the stiffness coefficient. For this purpose, a necessary method via “the measure of noncompactness” is established.

Existence and upper semicontinuity of pullback attractors for Kirchhoff wave equations in time-dependent spaces

“…Yang and Li [18] obtained the process generated by problem u tt −M ∇u 2 ∆u+ (−∆) α2 u t + f (u) = g(x, t) has pullback attractors for α 2 ∈ (1/2, 1) and the family of pullback attractors is upper semicontinuous in H 1 0 (Ω) ∩ L p+1 (Ω) × L 2 (Ω) when the nonlinearity f (u) is of supercritical growth p : 1 ≤ p < p α2 ≡ N +4α2 (N −4α2) + with N ≥ 3. In addition, Ma, Wang and Xie [11] verified the existence of pullback attractors for problem u tt − ∆u t − φ ∇u 2 ∆u + f (u) = h(x, t) in H 1 0 (Ω) × L 2 (Ω). Furthermore, Li, Yang and Feng [9] established the existence and continuity of uniform attractors for problem…”