Blow-up phenomena for a reaction diffusion equation with special diffusion process

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.