Overview
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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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
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.
Reviews
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Singularly Perturbed Boundary Value Problems
Book Subtitle: A Functional Analytic Approach
Authors: Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino
DOI: https://doi.org/10.1007/978-3-030-76259-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-76258-2Published: 05 October 2021
Softcover ISBN: 978-3-030-76261-2Published: 06 October 2022
eBook ISBN: 978-3-030-76259-9Published: 01 October 2021
Edition Number: 1
Number of Pages: XVI, 672
Number of Illustrations: 4 b/w illustrations
Topics: Partial Differential Equations, Ordinary Differential Equations, Operator Theory