Global attractors for plate equations with critical exponent in locally uniform spaces

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. In [14], the authors studied the existence of the random attractor for the stochastic strongly damping plate equations with additive noise and critical nonlinearity.…”

Global Attractor for Some Beam Equation With Nonlinear Source and Damping Terms

“…The existence of attractor for wave equation with critical exponent was obtained in [8,9,18,19]. Nakao [12] dealt with the global attractor of the quasi-linear wave equation with a strong dissipation.…”

Existence of the global attractor for the plate equation with nonlocal nonlinearity in $ \mathbb{R} ^{n}$

“…In the case of unbounded domains, owing to the lack of Sobolev compact embedding theorems, there are difficulties in applying the methods given for bounded domains. In order to overcome these difficulties, the authors of [9][10], [13] and [23] established the uniform tail estimates for the plate equations with local nonlinearities and then used the weak continuity of the nonlinear source operators.…”