Blow-up phenomena for some nonlinear parabolic problems

We consider the blow-up of solutions of equations of the form

_ut=div(ρ(|∇u|²) grad u)+f(u)$u_t=\text{div}\left(\rho \left({\left|\nabla u\right|}^2\right)\text{ grad }u\right)+f\left(u\right)$

by means of a differential inequality technique. A lower bound for blow-up time is determined if blow-up does occur as well as a criterion for blow-up and conditions which ensure that blow-up cannot occur.