Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping

Stochastic nonlinear beam equations

“…It is not obvious that solutions to (0.1) do not blow up at finite time, however, the equation (0.1) as well as its abstract version discussed below have already attracted considerable attention and their properties are rather well understood nowadays. Let us quote at least the papers [1], [24], [16], [32], [20] and [33], in which nonexplosion results and further references may be found. Motivated by problems arising in aeroelasticity (the description of large amplitude vibrations of an elastic panel excited by aerodynamic forces), Chow and Menaldi in [8] considered a beam described by the equation (0.1) and subjected to a force including random fluctuations.…”

“…If σ ≡ 0, many results on the stabilizing effect of nonlinear damping terms are available (see e.g. [7], [9], [13], [15], [20], [33] for various stability results). Stability of the zero solution of stochastic evolution equations has been studied recently in many papers, but mainly in the parabolic case (see e.g.…”

Uniform attractors for a nonautonomous extensible plate equation with a strong damping

“…Yang [13] studied the existence of finite-dimensional global attractors and exponential attractors. For more results, one can refer to [15][16][17][18][19] and the references therein.In this paper, we pay attention to the uniform attractors of (1.1) where main features are presented in the following:1. To our best knowledge, there are some interesting results of existence of global attractors and pullback attractors, but fewer work of uniform attractors for the extensible plate equation with a strong damping.…”

“…Yang [13] studied the existence of finite-dimensional global attractors and exponential attractors. For more results, one can refer to [15][16][17][18][19] and the references therein.…”

Energy decay of dissipative plate equations with memory-type boundary conditions

“…In Ammari and Tucsnak [4], Cavalcanti et al [7], Guzman and Tucsnak [11], Komornik [18], Pazoto et al [39], and Vasconcellos and Teixeira [41], it was proved that if h satisfies where c 1 , c 2 are positive constants, then for q = 1 the energy decay rate is exponential while for q > 1 we obtain a polynomial decay rate. Similar results were also obtained for boundary frictional damping (see Horn [14], Komornik [19], Lagnese [21], Lasiecka [22], and Ji and Lasiecka [15]).…”