Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
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DOI：
10.1515/9783110960716
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
S. Kabanikhin;A. Satybaev;M. Shishlenin
中科院分区：
文献类型：
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作者：
S. Kabanikhin;A. Satybaev;M. Shishlenin
第一章主要定义和符号差分格式反演（FDSI）1.1.导言沃尔泰拉算子方程1.3.定义和示例1.4. FDSI的收敛性1.5.第2章：第二章波动方程的线性化多维反问题2.1.导言问题公式化2.3.线性化2.4分析一维正问题解的结构2.5.直接问题的存在定理2.6.逆问题的解的唯一性和正则化2.7.数值例子vi求解多维反问题的直接方法第3章. I.M.的方法Gel'fand，B.M. Levitan和M. G.克莱因3.1。导言3.2.一维反问题的GLK方程
Main definitions and notations Introduction Chapter 1. Finite-difference scheme inversion (FDSI) 1.1. Introduction 1.2. Volterra operator equations 1.3. Definitions and examples 1.4. Convergence of FDSI 1.5. Numerical examples Chapter 2. Linearized multidimensional inverse problem for the wave equation 2.1. Introduction 2.2. Problem formulation 2.3. Linearization 2.4 Analyzing the structure of the solution to one-dimensional direct problem 2.5. Existence theorem for the direct problem 2.6. Uniqueness of solutions to the inverse problem and regularization 2.7. Numerical examples vi Direct Methods of Solving Multidimensional Inverse Problems Chapter 3. Methods of I.M. Gel'fand, B.M. Levitan and M. G. Krein 3.1. Introduction 3.2. Gel'fand-Levitan-Krein (GLK) equation for one-dimensional inverse problem