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.
, Yaroslav Kurylev
, Matti Lassas
Chapman & Hall/CRC
Country of Publication:
Series: Monographs and Surveys in Pure and Applied Mathematics
30 July 2001
Professional and scholarly
Professional & Vocational
A / AS level
Further / Higher Education
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.
Kachalov, Alexander; Kurylev, Yaroslav; Lassas, Matti
Reviews for Inverse Boundary Spectral Problems
[This book] contains a wealth of important methods and ideas, and the presentation is always very clear. [A] very interesting and valuable contribution to the literature on inverse problems for partial differential equations. - Zentralblatt MATH, Vol. 1037