A weak solution concept for the Dirichlet problem in
bounded domains for the degenerate parabolic equation
$u_t = f(u)\Delta u$
is presented. It is shown that if
$\int_0^1 \frac{ds}{f(s)}<\infty$
then each nontrivial nonnegative weak solution eventually becomes positive,
while if $\int_0^1 \frac{ds}{f(s)} = \infty$
then all weak solutions have their support constant
in time.
