| Description |
1 online resource (214 pages) |
| Series |
Inverse and ill-posed problems series |
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Inverse and ill-posed problems series.
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| Contents |
880-01 Chapter 1. Basic concepts of ill-posed problem theory -- 1.1. Classical well-posedness and Tikhonov'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 space |
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880-01/(N Frontmatter -- Preface -- Contents -- Chapter 1. Basic Concepts of Ill-Posed Problem Theory -- Chapter 2. Linear Volterra Operators and their Properties -- Chapter 3. Linear Operator Volterra Equations -- Chapter 4. Nonlinear Operator Volterra Equations in the Scales of Banach Spaces -- Chapter 5. Abstract Integro-Differential Equations and Inverse Problems -- Chapter 6. Multidimensional Inverse Problems -- Chapter 7. Multidimensional Integro-Differential Equations оf Volterra Type -- Chapter 8. Inverse Problems of Wave Propagation and Scattering -- Bibliography |
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2.3. Operators JÜ and their properties -- 2.4. Classical uniqueness and stability theorems -- 2.5. v(A) estimates and v-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 spaces |
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4.1. 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 kernels -- Chapter 6. Multidimensional inverse problems |
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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 equations -- 8.3. Statement of the inverse scattering on the barrier problems |
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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 |
| Summary |
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed July 11, 2017) |
| Subject |
Volterra equations.
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Integral equations.
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Inverse problems (Differential equations)
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Integral equations
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Inverse problems (Differential equations)
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Volterra equations
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| Form |
Electronic book
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| ISBN |
9783110943245 |
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3110943247 |
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