Multiple-Scale Analysis of Boundary-Value Problems in Thick Multi-Level Junctions of Type 3:2:2

Taras A. Mel'nyk is Professor in the Mathematical Physics Department of the Faculty of Mechanics and Mathematics at Taras Shevchenko National University of Kyiv, where he has developed a number of special courses on topics such as asymptotic methods in mathematical physics and the theory of homogenization. A fellow of the Alexander von Humboldt Foundation and member of the American Mathematical Society, he is the author of the textbooks "Complex Analysis" (2015) and "Sobolev Space Theory and Weak Solutions of Boundary Value Problems" (2018). His research interests are related to asymptotic analysis of boundary-value problems, spectral problems, variational inequalities, optimal control problems in domains with complex micro-inhomogeneous structure (perforated materials, composite materials, thick multi-structures, domains with rapidly oscillating boundaries, domains with concentrated masses, thin domains, thin graph-like junctions). Dmytro Yu. Sadovyi is a postdoctoral researcher at Taras Shevchenko National University of Kyiv, where he obtained his PhD in 2014. His current research interests lie in homogenization of boundary-value problems in thick multi-level junctions.

1 Introduction.- 2 Homogenization of Linear Elliptic Problems.- 3 Homogenization of Elliptic Problems in Thick Junctions with Sharp Edges.- 4 Homogenization of Semilinear Parabolic Problems.- 5 Asymptotic Approximations for Solutions to Semilinear Problems.- References.

"The book is well organized and each chapter contains a conclusion with comments and physical interpretation and can be useful to researchers and graduate students interested in asymptotic analysis and applied mathematics." (Paolo Musolino, zbMATH 1443.35004, 2020)