Asymptotic dynamics of plate equations with a critical exponent on unbounded domain

Regularity and finite dimensionality of attractor for plate equation on R n

“…We denote by S t the semigroup defined in H 2 × L 2 by the Cauchy problem (11)-(12). Please refer to [2] for details.…”

“…There are sufficient conditions ensuring (4)-(6) (please refer to [2] for details). In [2], the authors studied asymptotic dynamics of (1) in the phase space H 2 × L 2 .…”

“…In [2], the authors studied asymptotic dynamics of (1) in the phase space H 2 × L 2 . For details, we established the following result.…”

Global Attractors of the Extensible Plate Equations with Nonlinear Damping and Memory

“…In the case where ( ) ≡ 0, = = 0, (1) becomes the normal plate equation which has been treated in many papers such as [7][8][9][10][11][12][13][14]. For instance, the authors investigated the existence of the compact attractor for the plate equation on both the bounded domain [8,10,13] and the unbounded domain in [7,11,12], respectively.…”

“…For instance, the authors investigated the existence of the compact attractor for the plate equation on both the bounded domain [8,10,13] and the unbounded domain in [7,11,12], respectively. Yue and Zhong [9] proved the existence of global attractors to the plate equations when the nonlinear function satisfies the critical exponent in a locally uniform space.…”