Inverse Boundary Spectral Problems: 1st Edition (Paperback) book cover

Inverse Boundary Spectral Problems

1st Edition

By Alexander Kachalov, Yaroslav Kurylev, Matti Lassas

Chapman and Hall/CRC

312 pages

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Inverse boundary problems are a rapidly developing area of applied mathematics with applications throughout physics and the engineering sciences. However, the mathematical theory of inverse problems remains incomplete and needs further development to aid in the solution of many important practical problems.

Inverse Boundary Spectral Problems develop a rigorous theory for solving several types of inverse problems exactly. In it, the authors consider the following:

"Can the unknown coefficients of an elliptic partial differential equation be determined from the eigenvalues and the boundary values of the eigenfunctions?"

Along with this problem, many inverse problems for heat and wave equations are solved.

The authors approach inverse problems in a coordinate invariant way, that is, by applying ideas drawn from differential geometry. To solve them, they apply methods of Riemannian geometry, modern control theory, and the theory of localized wave packets, also known as Gaussian beams. The treatment includes the relevant background of each of these areas.

Although the theory of inverse boundary spectral problems has been in development for at least 10 years, until now the literature has been scattered throughout various journals. This self-contained monograph summarizes the relevant concepts and the techniques useful for dealing with them.

Table of Contents

One-Dimensional Problem. Basic Geometrical and Analytical Methods for Inverse Problems. Gel'fand Inverse Boundary Spectral Problem for Manifolds. Inverse Problems for Wave and other Types of Equations. Bibliography. Table of Notation.

About the Authors

Kachalov, Alexander; Kurylev, Yaroslav; Lassas, Matti

About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations
SCIENCE / Mathematical Physics