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© 2008

Boundary Integral Equations

Book

Part of the Applied Mathematical Sciences book series (AMS, volume 164)

About this book

Introduction

This book is devoted to the basic mathematical properties of solutions to boundary integral equations and presents a systematic approach to the variational methods for the boundary integral equations arising in elasticity, fluid mechanics, and acoustic scattering theory. It may also serve as the mathematical foundation of the boundary element methods. The latter have recently become extremely popular and efficient computational tools in applications. The authors are well known for their fundamental work on boundary integral equations and related topics. This book is a major scholarly contribution to the modern theory of boundary integral equations and should be accessible and useful to a large community of mathematical analysts, applied mathematicians, engineers and scientists.

Keywords

Fredholm alternative Garding' s inequality Green' s formulae Integral equation differential equation first kind and second kind integral equations fluid mechanics fundamental solutions mechanics operator pseudo-differential operators scattering

Authors and affiliations

  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Institut für Angewandte Analysis und Numerische SimulationUniversität Stuttgart70569Germany

Bibliographic information

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Reviews

From the reviews:

"The main goal of this book is to explain the mathematical foundation of the boundary element methods (BEMs) … . The BEM is well developed and widely used by engineers and scientists in applied mathematical computations for 40 years. … The book will be helpful not only for mathematicians who want to become familiar with the BIE but also for users of BEMs who want to understand mathematical background of the computational method." (Vladimir Sládek, Zentralblatt MATH, Vol. 1157, 2009)

"This book has been in preparation for many years: the care in its composition is evident. … The development of … analytical framework occupies the major part of this impressive book. … There are 10 chapters and a bibliography of 325 items. … In summary, this is an important scholarly work on the modern mathematical theory of boundary integral equations." (Paul Andrew Martin, Mathematical Reviews, Issue 2009 i)