  We consider a fourth order evolution equation involving a singular nonlinear
term $\frac{\lambda}{(1-u)^{2}}$ in a bounded domain $\Omega\subset\R^{n}$.
This equation arises in the modeling of microelectromechanical systems. We
first investigate the well-posedness of a fourth order parabolic equation which
has been studied in \cite{Lau}, where the authors, by the semigroup argument,
obtained the well-posedness of this equation for $n\leq2$. Instead of semigroup
method, we use the Faedo-Galerkin technique to construct a unique solution of
the fourth order parabolic equation for $n\leq7$, which improves and completes
the result of \cite{Lau}. Besides, the well-posedness of the corresponding
fourth order hyperbolic equation is obtained by the similar argument for
$n\leq7$.
