  In this work we analyze the boundedness properties of the solutions of a
nonautonomous parabolic degenerate logistic equation in a bounded domain. The
equation is degenerate in the sense that the logistic nonlinearity vanishes in
a moving region, $K(t)$, inside the domain. The boundedness character of the
solutions depends not only on, roughly speaking, the first eigenvalue of the
Laplace operator in $K(t)$ but also on the way this moving set evolves inside
the domain and in particular on the speed at which it moves.
