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© 2019

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

Book

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Taras Mel’nyk, Dmytro Sadovyi
    Pages 1-12
  3. Taras Mel’nyk, Dmytro Sadovyi
    Pages 13-30
  4. Taras Mel’nyk, Dmytro Sadovyi
    Pages 51-72
  5. Back Matter
    Pages 97-105

About this book

Introduction

This book presents asymptotic methods for boundary-value problems (linear and semilinear, elliptic and parabolic) in so-called thick multi-level junctions. These complicated structures appear in a large variety of applications.

A concise and readable introduction to the topic, the book provides a full review of the literature as well as a presentation of results of the authors, including the homogenization of boundary-value problems in thick multi-level junctions with non-Lipschitz boundaries, and the construction of approximations for solutions to semilinear problems.

Including end-of-chapter conclusions discussing the results and their physical interpretations, this book will be of interest to researchers and graduate students in asymptotic analysis and applied mathematics as well as to physicists, chemists and engineers interested in processes such as heat and mass transfer.

Keywords

homogenization multiple-scale analysis asymptotic approximations of solutions boundary value problems nonlinear perturbed boundary conditions domains with rapidly oscillating boundaries multi-level thick junctions non-Lipschitz boundaries

Authors and affiliations

  1. 1.Faculty of Mechanics and MathematicsTaras Shevchenko National University of KyivKyivUkraine
  2. 2.Faculty of Mechanics and MathematicsTaras Shevchenko National University of KyivKyivUkraine

About the authors

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.

Bibliographic information

Reviews

“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)