Volterra equations and inverse problems

Volterra equations and inverse problems / A.L. Bughgeim.

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Bibliographic Details
Main Author: Bukhgeĭm, A. L. (Aleksandr Lʹvovich) (Author)
Format: eBook
Language:English
Published: Utrecht, the Netherlands : VSP, 1999.
Series:Inverse and ill-posed problems series.
Subjects:
Volterra equations.
Inverse problems (Differential equations)
Volterra equations
Online Access:Click for online access
Table of Contents:
  • Chapter 1. Basic concepts of ill-posed problem theory
  • 1.1. Classical well-posedness and Tikhonovâ€?s well-posedness
  • 1.2. Simplest properties of the well-posedness set and the continuity modulus. Connection with estimates of the interpolation type
  • 1.3. Projection on the convex closed set. Quasisolution
  • 1.4. The structure of correctness sets
  • 1.5. Regularizators and regularising operator sets
  • 1.6. Final remarks
  • Chapter 2. Linear Volterra operators and their properties
  • 2.1. Abstract Volterra operators
  • 2.2. Completely continuous Volterra operators in a Hilbert space2.3. Operators Jα and their properties
  • 2.4. Classical uniqueness and stability theorems
  • 2.5. Ï?(Î?) estimates and Ï?-continuity criteria
  • Chapter 3. Linear operator Volterra equations
  • 3.1. Operator Volterra equations in the scales of Banach spaces
  • 3.2. Operator Volterra equations of the first kind
  • 3.3. Operator Volterra equation of the first kind with the nondifferentiable kernel
  • 3.4. Examples of scales of Banach spaces
  • 3.5. Examples of operator Volterra equations
  • Chapter 4. Nonlinear operator Volterra equations in the scales of Banach spaces4.1. Formulations of the basic theorems
  • 4.2. Definitions and auxiliary statements
  • 4.3. Proofs of the basic theorems
  • 4.4. Inverse kinematic problem of seismology
  • Chapter 5. Abstract integro-differential equations and inverse problems
  • 5.1. Basic estimates
  • 5.2. Uniqueness and stability of solution of integro-differential equations and inequalities
  • 5.3. The problem of determining the right side of the evolutionary equation
  • 5.4. Evolutionary equation of the second order
  • 5.5. Operator Volterra equations with commuting kernelsChapter 6. Multidimensional inverse problems
  • 6.1. Inverse problems, commutators and a priori estimates
  • 6.2. Theorems of decomposition
  • 6.3. Examples of inverse problems that admit decomposition
  • Chapter 7. Multidimensional integro-differential equations of Volterra type
  • 7.1. Statement of the problem
  • 7.2. Necessary conditions
  • 7.3. Sufficient conditions
  • Chapter 8. Inverse problems of wave propagation and scattering
  • 8.1. The inverse problem of wave propagation in layered media
  • 8.2. The problem of determining the right side of the Lameé equations8.3. Statement of the inverse scattering on the barrier problems
  • 8.4. Definitions and auxiliary facts
  • 8.5. Uniqueness of the inverse scattering problem in the Kirchhoff approximation
  • 8.6. Problems of coefficients determination
  • Bibliography

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