Dependence of the blow‐up time with respect to parameters and numerical approximations for a parabolic problem

Abstract

We find a bound for the modulus of continuity of the blow‐up time for the problem u_t=λΔu+u^p, with initial datum u(x,0)=ϕ(x)+hf(x) respect to the parameters λ, p and h. We also find an estimate for the rate of convergence of the blow‐up times for a semi‐discrete numerical scheme.