  We present results for finite time blow-up for filtration problems with
nonlinear reaction under appropriate assumptions on the nonlinearities and the
initial data. In particular, we prove first finite time blow up of solutions
subject to sufficiently large initial data provided that the reaction term
"overpowers" the nonlinear diffusion in a certain sense. Secondly, under
related assumptions on the nonlinearities, we show that initial data above
positive stationary state solutions will always lead to finite time blow up.
