Inverse Boundary Spectral Problems
Inverse Boundary Spectral Problems
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DOI：
10.1201/9781420036220
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发表时间：
2001-07
期刊：
影响因子：
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通讯作者：
A. Katchalov;Y. Kurylev;M. Lassas
中科院分区：
文献类型：
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作者：
A. Katchalov;Y. Kurylev;M. Lassas
© 2001 Chapman & Hall/CRC 版权所有。逆边界问题是应用数学的一个快速发展的领域，其应用遍及物理学和工程科学。然而，反问题的数学理论仍然不完整，需要进一步发展以帮助解决许多重要的实际问题。逆边界谱问题发展了一种严格的理论来精确解决几种类型的逆问题。在其中，作者考虑了以下问题：“椭圆偏微分方程的未知系数可以根据特征值和特征函数的边界值确定吗？”除了这个问题之外，许多热方程和波动方程的反问题也得到了解决。作者以坐标不变的方式处理逆问题，即应用微分几何的思想。为了解决这些问题，他们应用了黎曼几何、现代控制理论和局域波包理论（也称为高斯光束）的方法。治疗包括每个领域的相关背景。尽管逆边界谱问题的理论已经发展了至少 10 年，但到目前为止，文献还分散在各种期刊中。这本独立的专着总结了相关概念和处理这些概念的有用技术。
© 2001 by Chapman & Hall/CRC. 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.