Uniform approximation of solutions of nonlinear parabolic problems in perforated domains

  • A. V. Zhuravskaya
  • I. V. Skrypnik


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.
How to Cite
Zhuravskaya, A. V., and I. V. Skrypnik. “Uniform Approximation of Solutions of Nonlinear Parabolic Problems in Perforated Domains”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 9, Sept. 2004, pp. 1244-58, https://umj.imath.kiev.ua/index.php/umj/article/view/3838.
Research articles