Uniform approximation of solutions of nonlinear parabolic problems in perforated domains - Zhuravskaya, A. V.; Skrypnik, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We investigate the behavior of a remainder of an asymptotic expansion for solutions of a quasi-linear parabolic Cauchy-Dirichlet problem in a sequence of domains with fine-grained boundary. By using a modification of an asymptotic expansion and new pointwise estimates for a solution of a model problem, we prove the uniform convergence of the remainder to zero.