Overview
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.
Full Product Details
Author: Taras Mel'nyk ,
Dmytro Sadovyi
Publisher: Springer Nature Switzerland AG
Imprint: Springer Nature Switzerland AG
Edition: 1st ed. 2019
Weight: 0.454kg
ISBN: 9783030355364
ISBN 10: 3030355365
Pages: 105
Publication Date: 07 February 2020
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
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)
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)
Author Information
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.
