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Inverse Boundary Spectral Problems - Monographs and Surveys in Pure and Applied Mathematics Alexander Kachalov 1st edition
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Inverse Boundary Spectral Problems - Monographs and Surveys in Pure and Applied Mathematics
Alexander Kachalov
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.
312 pages
| Media | Books Paperback Book (Book with soft cover and glued back) |
| Released | September 23, 2019 |
| ISBN13 | 9780367397050 |
| Publishers | Taylor & Francis Ltd |
| Pages | 312 |
| Dimensions | 150 × 220 × 10 mm · 430 g |
| Language | English |
