Layer Potential Techniques in Spectral Analysis

Description

Since the early part of the twentieth century, the use of integral equations has developed into a range of tools for the study of partial differential equations. This includes the use of single- and double-layer potentials to treat classical boundary value problems. The aim of this book is to give a self-contained presentation of an asymptotic theory for eigenvalue problems using layer potential techniques with applications in the fields of inverse problems, band gap structures, and optimal design, in particular the optimal design of photonic and phononic crystals. Throughout this book, it is shown how powerful the layer potentials techniques are for solving not only boundary value problems but also eigenvalue problems if they are combined with the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. The general approach in this book is developed in detail for eigenvalue problems for the Laplacian and the Lame system in the following two situations: one under variation of domains or boundary conditions and the other due to the presence of inclusions. The book will be of interest to researchers and graduate students working in the fields of partial differential equations, integral equations, and inverse problems. Researchers in engineering and physics may also find this book helpful.

Get the book

Amazon.com

Search the book

eBay.com

Search the book

Similar books

• 

  The Boundary Integral Approach to Static and Dynamic Contact Problems: Equality and Inequality Methods

  By Heinz Antes, P. D. Panagiotopoulos, Panagiotis P. Panagiotopoulos

  In many B.V.Ps we shall encounter the boundary condition written for u € [ H ( 2 ) ] and S € ( H - 1 / 2 ( T ) ] in the form Ø ( yu ) - ( yu ) 2 ( -5 , yu – yu ) , Vo € [ H ( 12 ) ] ?. ( 1.115a ) Since the trace application v + yv is ...

• 

  Advances in Boundary Elements: Field and fluid flow solutions

  By Jerome J. Connor, C. A. Brebbia

  is by Longuet-Higgins and Cokelet [1], who considered space- periodic, steep surface waves. They constructed a mixed Eulerian- Lagrangian method where the flux at the surface is obtained via an indirect-type boundary integral equation ...

• 

  Boundary Elements IX

  By C. A. Brebbia, Wolfgang L. Wendland, G. Kuhn

  Longuet - Higgins and Cokelet succeeded to derive plunging breakers by transformation of the infinite fluid problem to a problem having a finite boundary . The same approach has been used in Srokosz15 to study the interaction of ...

• 

  Design-sensitivity Analysis

  By Michał Kleiber, T. Hisada

  Design-sensitivity Analysis