Uniform approximation of solutions of nonlinear parabolic problems in perforated domains
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.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 9, pp 1481-1498.
Citation Example: Skrypnik I. V., Zhuravskaya A. V. Uniform approximation of solutions of nonlinear parabolic problems in perforated domains // Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1244-1258.