In this paper, we consider the following initial-boundary value problem

where Ω is a bounded domain in with smooth boundary ∂Ω, λ is a positive parameter, L is an elliptic operator, on  is a  convex, increasing function,  is a function,  Under some assumptions, we show that the solution of the above problem blows up in a finite time, and its blow-up time goes to that of the solution of the following differential equation

as λ tends to infinity, where  We also extend the above result to other classes of nonlinear reaction diffusion equations with nonlinear boundary conditions. Finally, we give some numerical results to illustrate our analysis.

nonlinear equations, nonlinear boundary conditions, blowup, numerical blow-up time.