chapter  14
Asymptotic Behavior and the Existence of Finite-Dimensional Attractors for von Karman Plate Equations with Boundary Damping
Pages 22

Function F G L 2( i i ) represents the action of a load/force applied to the plate, and functions /¿,g are monotone increasing and continuous. x (ii;)-A iry ’s stress function satisfies the system of equations

A 2x = —[w,w]\ in X = l:X = 0 on

With the dynamics described by (1.1) we associate the following energy function

(1.3) E ( t ) = { K P + 72|Vu>i|2}d f t + \ j r w2d^ + \ a(w’ w)

+ \ f \^x (w )2dfl,2 JQ

where a{w, w) = j n |Aw|2 + (1 - n)[2w2xy - w2xx - w2y}dtt. We also define the Hilbert space H = H 2(Vt) x H l (Vi) endowed with a norm

The following well-posedness result is available.