Bounds for blow-up time in nonlinear parabolic problems

A first order differential inequality technique is used on suitably defined auxiliary functions to determine lower bounds for blow-up time in initial-boundary value problems for parabolic equations of the formut=div(ρ(u)gradu)+f(u)ut=div(ρ(u)gradu)+f(u) if blow-up occurs. In addition, conditions which ensure that blow-up occurs or does not occur are presented.