Numerical analysis of the rescaling method for parabolic problems with blow-up in finite time

摘要

In this work, we study the numerical solution for parabolic equations whosesolutions have a common property of blowing up in finite time and the equationsare invariant under the following scaling transformation $$u \mapstou_\lambda(x,t):= \lambda^{\frac{2}{p-1}}u(\lambda x, \lambda^2 t).$$ For thatpurpose, we apply the rescaling method proposed by Berger and Kohn in 1988 tosuch problems. The convergence of the method is proved under some regularityassumption. Some numerical experiments are given to derive the blow-up profileverifying henceforth the theoretical results.