Bounds for the Blow-up Time and Blow-up Rate Estimates for Nonlinear Parabolic Equations with Dirichlet or Neumann Boundary Conditions

This paper is concerned with the blow-up phenomena for a type of parabolic equations withweighted nonlinear source(b(u))t= div(|∇u|p−2∇u) +f(x,u), x∈Ω,t >0,u(x,t) = 0 or∂u∂n= 0,x∈∂Ω,t >0,u(x,0) =g(x)≥0,x∈Ω,where Ω⊂RN(N≥3) is a smooth bounded domain. Through constructing some suitableauxiliary functions and using the first-order differential inequality technique, we obtain the boundsfor the blow-up time and the estimates of the blow-up rate of the solution to the problem.