Dynamic von Karman equations with viscous damping

In this paper we are interested to the dynamic von Karman equations coupled with viscous damping and without rotational forces, $(\alpha =0)$ [Chueshov I., Lasiecka I. (2010)], this problem describes the buckling and flexible phenomenon of small nonlinear vibration of vertical displacement to the elastic plates.  Our fundamental goal is to establish the existence and the uniqueness to the weak solution for the so-called global energy, under assumption $F_0\in H^{3+\epsilon}(\omega)$.  Finally for illustrate our theoretical results we use the finite difference method.