Singularly Perturbed Boundary Value Problems

A Functional Analytic Approach

Authors: Dalla Riva, Matteo, Lanza de Cristoforis, Massimo, Musolino, Paolo

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  • Presents the effect of perturbations in terms of analytic functions instead of in terms of the more classical asymptotic expansions
  • Shows a powerful tool for the analysis of nonlinear and non-variational boundary value problems
  • Presents a step-by-step exposition from the theoretical foundations of the Functional Analytic Approach to the implementation in challenging problems
  • Provides an effective tool in the analysis of specific perturbation problems arising in continuum mechanics and material sciences
  • Introductory style is accessible to a wide readership
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  • ISBN 978-3-030-76259-9
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Hardcover $179.99
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About this book

This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains.  The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis.

Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems.  The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.

About the authors

​Matteo Dalla Riva is professor at College of Engineering and Natural Science in The University of Tulsa.
Massimo Lanza de Cristoforis is professor at Dipartimento di Matematica Universita` degli Studi di Padova.
Paolo Musolino is professor at Dipartimento di Scienze Molecolari e Nanosistemi Università Ca' Foscari Venezia.



Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook $139.00
price for USA in USD
  • ISBN 978-3-030-76259-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.99
price for USA in USD
  • ISBN 978-3-030-76258-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Singularly Perturbed Boundary Value Problems
Book Subtitle
A Functional Analytic Approach
Authors
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-76259-9
DOI
10.1007/978-3-030-76259-9
Hardcover ISBN
978-3-030-76258-2
Edition Number
1
Number of Pages
XVI, 672
Number of Illustrations
4 b/w illustrations
Topics