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Singularly Perturbed Boundary Value Problems

A Functional Analytic Approach de

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Springer


Paru le : 2021-10-01

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Description

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.
Pages
672 pages
Collection
n.c
Parution
2021-10-01
Marque
Springer
EAN papier
9783030762582
EAN PDF
9783030762599
Informations sur l'ebook
Nombre pages copiables
6
Nombre pages imprimables
67
Taille du fichier
8131 Ko
Prix
158,24 €
EAN EPUB
9783030762599
Informations sur l'ebook
Nombre pages copiables
6
Nombre pages imprimables
67
Taille du fichier
62536 Ko
Prix
158,24 €

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