  This paper is concerned with the blow-up property of solutions to an initial
boundary value problem for a reaction diffusion equation with special diffusion
processes. It is shown, under certain conditions on the initial data, that the
solutions to this problem blow up in finite time, by combining Hardy
inequality, "moving" potential well methods with some differential
inequalities. Moreover, the upper and lower bounds for the blow-up time are
also derived when blow-up occurs.
