Global attractor for a nonlinear plate equation with supported boundary conditions

Abstract

In this paper, we consider a two-dimensional nonlinear equationwhich arises from the model of the viscoelastic thin rectangular plate with four edges supported. By virtue of Galerkin method combined with the priori estimates, we prove the existence and uniqueness of the global solution under initial-boundary data for the above equation. Especially the existence of the bounded absorbing set in space E and the existence of the global attractor of system is also obtained.

Long-time behavior of a model of extensible beams with nonlinear boundary dissipations

“…We quote, for instance, Ball [8,9], Dickey [10,11] and Medeiros [12], considered as pioneering works. Other interesting contributions can be found in, for instance, [13,14,5,6,[15][16][17][18][19] and the references therein.…”

A nonlinear plate control without linearization

“…In this study, the vibration control problem for a nonlinear plate is considered as follows [2]; is the plate rigidity in which E; h and v are modulus of elasticity, plate thickness and Poisson's ratio, respectively, is the material density, T is the normal load per unit area, > 0 is a small parameter, is the damping coefficient of the plate and…”

“…In [2], existence and uniqueness of the solution to the nonlinear homogeneous plate equation is given. In order to ensure integrity of the present study, let us recall the existence of the solution.…”

“…Then, w.t / is a weak solution of the system under consideration (see [1,2]). By introducing the following lemma, let us show that the system given by Eqs.…”

Integrodifferential equations with applications to a plate equation with memory

“…Plate equations with or without memory effects have been attracted many researchers with various purposes. See [14]- [18], [22], [24], [26], [29], [31], [32] and references therein. Precisely, we present results concerning to the existence, uniqueness, regularity, unique continuation, blow-up alternative and continuous dependence of mild solutions to the strongly damped plate equation with memory (1.1)-(1.3).…”