  Let $\Omega$ be a smooth bounded domain in $\R^n$, $n\ge 5$. We consider the
semilinear heat equation at the critical Sobolev exponent $$ u_t = \Delta u +
u^{\frac{n+2}{n-2}} \inn \Omega\times (0,\infty), \quad u =0 \onn
\pp\Omega\times (0,\infty). $$
  Let $G(x,y)$ be the Dirichlet Green's function of $-\Delta$ in $\Omega$ and
$H(x,y)$ its regular part. Let $q_j\in \Omega$, $j=1,\ldots,k$, be points such
that the matrix $$
  \left [ \begin{matrix} H(q_1, q_1) & -G(q_1,q_2) &\cdots & -G(q_1, q_k)
-G(q_1,q_2) & H(q_2,q_2) & -G(q_2,q_3) \cdots & -G(q_3,q_k) \vdots & & \ddots&
\vdots -G(q_1,q_k) &\cdots& -G(q_{k-1}, q_k) & H(q_k,q_k) \end{matrix} \right ]
$$ is positive definite. For any $k\ge 1$ such points indeed exist. We prove
the existence of a positive smooth solution $u(x,t)$ which blows-up by bubbling
in infinite time near those points. More precisely, for large time $t$, $u$
takes the approximate form $$ u(x,t) \approx \sum_{j=1}^k \alpha_n \left (
\frac { \mu_j(t)} { \mu_j(t)^2 + |x-\xi_j(t)|^2 } \right )^{\frac {n-2}2} . $$
Here $\xi_j(t) \to q_j$ and $0<\mu_j(t) \to 0$, as $t \to \infty$. We find that
$\mu_j(t) \sim t^{-\frac 1{n-4}} $ as $t\to +\infty$, when $n\geq 5$.
