In this paper we analyze the porous medium equation
\begin{equation}\label{ProblemAbstract} \tag{◊} %\begin{cases}
u_t=\Delta u^m + a\io u^p-b u^q -c\lvert\nabla\sqrt{u}\rvert^2 \quad
\textrm{in}\quad \Omega \times I,%\\ %u_\nu-g(u)=0 & \textrm{on}\; \partial
\Omega, t>0,\\ %u({\bf x},0)=u_0({\bf x})&{\bf x} \in \Omega,\\ %\end{cases}
\end{equation} where Ω is a bounded and smooth domain of RN, with
N≥1, and I=[0,t∗) is the maximal interval of existence for u. The
constants a,b,c are positive, m,p,q proper real numbers larger than 1 and
the equation is complemented with nonlinear boundary conditions involving the
outward normal derivative of u. Under some hypothesis on the data, including
intrinsic relations between m,p and q, and assuming that for some positive
and sufficiently regular function u_0(\nx) the Initial Boundary Value Problem
(IBVP) associated to \eqref{ProblemAbstract} possesses a positive classical
solution u=u(\nx,t) on Ω×I: \begin{itemize} \item
[▹] when p>q and in 2- and 3-dimensional domains, we determine
a \textit{lower bound of} t∗ for those u becoming unbounded in
Lm(p−1)(Ω) at such t∗; \item [▹] when p<q and in
N-dimensional settings, we establish a \textit{global existence criterion}
for u. \end{itemize