Asymptotic expansion of solutions of quasilinear parabolic problems in perforated domains

• Date: 1993
• Main Authors: Skrypnik, I. V., Скрыпник, И. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5961
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The asymptotic expansion of solutions to quasilinear parabolic problems with the Dirichlet boundary condilions is constructed in the regions with a fine-grain boundary. It is shown that the sequence of the remainders of the expansion strongly converges to zero in the space $W^{1,1/2}_2$.