Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
eBook - PDF

Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems

  1. 179 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems

About this book

The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.

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Yes, you can access Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems by Sergey I. Kabanikhin,Abdigany D. Satybaev,Maxim A. Shishlenin in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2013
Print ISBN
9789067644167
eBook ISBN
9783110960716
Edition
1
Topic
Mathematics
Subtopic
Differential Equations
Index
Mathematics

Table of contents

  1. Main definitions and notations
  2. Introduction
  3. Chapter 1. Finite-difference scheme inversion (FDSI)
  4. 1.1. Introduction
  5. 1.2. Volterra operator equations
  6. 1.3. Definitions and examples
  7. 1.4. Convergence of FDSI
  8. 1.5. Numerical examples
  9. Chapter 2. Linearized multidimensional inverse problem for the wave equation
  10. 2.1. Introduction
  11. 2.2. Problem formulation
  12. 2.3. Linearization
  13. 2.4. Analyzing the structure of the solution to one-dimensional direct problem
  14. 2.5. Existence theorem for the direct problem
  15. 2.6. Uniqueness of solutions to the inverse problem and regularization
  16. 2.7. Numerical examples
  17. Chapter 3. Methods of I. M. GePfand, B. M. Levitan and M. G. Krein
  18. 3.1. Introduction
  19. 3.2. Gel’fand-Levitan-Krein (GLK) equation for one-dimensional inverse problem
  20. 3.3. Multidimensional analog of GLK-equations
  21. 3.4. Gel’fand-Levitan method for wave equation
  22. 3.5. Discrete analog of the Gel'fand-Levitan equation
  23. 3.6. Multidimensional discrete analog
  24. 3.7. Numerical examples
  25. Chapter 4. Boundary control method (BC method)
  26. 4.1. Introduction. Statement of the problem
  27. 4.2. BC method in one-dimensional case
  28. 4.3. BC method for 2D acoustic inverse problem
  29. 4.4. Numerical examples
  30. Chapter 5. Projection method
  31. 5.1. Introduction
  32. 5.2. Projection method for solving inverse problem for the wave equation
  33. 5.3. Projection method for solving inverse acoustic problem
  34. 5.4. Numerical examples
  35. Appendix A
  36. Appendix B
  37. Bibliography