  This paper establishes the local exact controllability of the quasilinear
porous media equation with Dirichlet boundary condition.\\ Consider the
equation $$\begin{aligned} &y_t - \Delta a(y) = mu+f \text{ on } Q\\
&y(0)=y_0,\ y \mid_{\Sigma} = 0 \end{aligned}$$ on the $n+1$-dimensional
cylinder $Q = \Omega \times (0, T)$ with lateral boundary $\Sigma = \partial
\Omega \times (0, T)$. The exact controllability in finite time is proved when
$\|y_0 - y_s\|_{W^{1, n}_0(\Omega) \cap C(\overline \Omega)}$ is sufficiently
small, $n > 1$, for every stationary solution $y_s$ such that $a(y_s) \in W^{2,
q}(\Omega)$, where $q>n$. It is assumed that $\Omega$ is a bounded open set
with $C^2$ boundary and that $a \in C^2(\mathbb R)$, $a'>0$.
