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)ut=div(ρ(|∇u|2) grad u)+f(u) 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.