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Inverse Problems for Partial Differential Equations.

By: Isakov, Victor.
Material type: TextTextSeries: eBooks on Demand.Applied Mathematical Sciences: Publisher: Cham : Springer International Publishing, 2017Copyright date: ©2017Edition: 3rd ed.Description: 1 online resource (414 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9783319516585.Subject(s): Computer science_xMathematicsGenre/Form: Electronic books.Additional physical formats: Print version:: Inverse Problems for Partial Differential EquationsDDC classification: 515.353 Online resources: Click here to view this ebook.
Contents:
Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Chapter 1 Inverse Problems -- 1.1 The Inverse Problem of Gravimetry -- 1.2 The Inverse Conductivity Problem -- 1.3 Inverse Scattering -- 1.4 Tomography and the Inverse Seismic Problem -- 1.5 Inverse Spectral Problems -- Chapter 2 Ill-Posed Problems and Regularization -- 2.1 Well- and Ill-Posed Problems -- 2.2 Conditional Correctness: Regularization -- 2.3 Construction of Regularizers -- 2.4 Convergence of Regularization Algorithms -- 2.5 Iterative Algorithms -- Chapter 3 Uniqueness and Stability in the CauchyProblem -- 3.1 The Backward Parabolic Equation -- 3.2 General Carleman Estimates and the Cauchy Problem -- 3.3 Elliptic and Parabolic Equations -- 3.4 Hyperbolic and Schrödinger Equations -- 3.5 Systems of Partial Differential Equations -- 3.6 Open Problems -- Chapter 4 Elliptic Equations: Single BoundaryMeasurements -- 4.0 Results on Elliptic Boundary Value Problems -- 4.1 Inverse Gravimetry -- 4.2 Reconstruction of Lower-Order Terms -- 4.3 The Inverse Conductivity Problem -- 4.4 Methods of the Theory of One Complex Variable -- 4.5 Linearization of the Coefficient Problem -- 4.6 Some Problems of Detection of Defects -- 4.7 Open Problems -- Chapter 5 Elliptic Equations: Many BoundaryMeasurements -- 5.0 The Dirichlet-to-Neumann Map and theCauchy Set -- 5.1 Boundary Reconstruction -- 5.2 Completeness of Products of Solutions of PDE -- 5.3 Uniqueness and Stability in Ω -- 5.4 Recovery of Several Coefficients -- 5.5 The Plane Case -- 5.6 Nonlinear Equations -- 5.7 Transmission Problems -- 5.8 Maxwell's and Elasticity Systems -- 5.9 Open Problems -- Chapter 6 Scattering Problems and Stationary Waves -- 6.0 Direct Scattering -- 6.1 From A to Near Field -- 6.2 The Inverse Source Problem with Many Wave Numbers -- 6.3 Scattering by a Medium.
6.4 Scattering by Obstacles -- 6.5 Open Problems -- Chapter 7 Integral Geometry and Tomography -- 7.1 The Radon Transform and its Inverse -- 7.2 The Energy Integral Methods -- 7.3 Boman's Counterexample -- 7.4 The Transport Equation -- 7.5 Open Problems -- Chapter 8 Hyperbolic Problems -- 8.0 Introduction -- 8.1 The One-Dimensional Case -- 8.2 Single Boundary Measurements -- 8.3 Many Measurements: The Use of Beam Solutions -- 8.4 Many measurements: Methods of BoundaryControl -- 8.5 Recovery of Discontinuity of the Speedof Propagation -- 8.6 Open Problems -- Chapter 9 Inverse Parabolic Problems -- 9.0 Introduction -- 9.1 Final Overdetermination -- 9.2 Lateral Overdetermination: Single Measurements -- 9.3 The Inverse Problem of Option Pricing -- 9.4 Lateral Overdetermination: Many Measurements -- 9.5 Discontinuous Principal Coefficient and Recovery of a Domain -- 9.6 Nonlinear Equations -- 9.7 Interior Sources -- 9.8 Open Problems -- Chapter 10 Some Numerical Methods -- 10.1 Numerics for the Cauchy Problem -- 10.2 Linearization -- 10.3 Relaxation Methods -- 10.4 Layer Stripping -- 10.5 Range Test Algorithms -- 10.6 Discrete Methods -- Appendix. Function Spaces -- References -- Index.
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Item type Current location Call number URL Status Date due Barcode
Electronic Book UT Tyler Online
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Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Chapter 1 Inverse Problems -- 1.1 The Inverse Problem of Gravimetry -- 1.2 The Inverse Conductivity Problem -- 1.3 Inverse Scattering -- 1.4 Tomography and the Inverse Seismic Problem -- 1.5 Inverse Spectral Problems -- Chapter 2 Ill-Posed Problems and Regularization -- 2.1 Well- and Ill-Posed Problems -- 2.2 Conditional Correctness: Regularization -- 2.3 Construction of Regularizers -- 2.4 Convergence of Regularization Algorithms -- 2.5 Iterative Algorithms -- Chapter 3 Uniqueness and Stability in the CauchyProblem -- 3.1 The Backward Parabolic Equation -- 3.2 General Carleman Estimates and the Cauchy Problem -- 3.3 Elliptic and Parabolic Equations -- 3.4 Hyperbolic and Schrödinger Equations -- 3.5 Systems of Partial Differential Equations -- 3.6 Open Problems -- Chapter 4 Elliptic Equations: Single BoundaryMeasurements -- 4.0 Results on Elliptic Boundary Value Problems -- 4.1 Inverse Gravimetry -- 4.2 Reconstruction of Lower-Order Terms -- 4.3 The Inverse Conductivity Problem -- 4.4 Methods of the Theory of One Complex Variable -- 4.5 Linearization of the Coefficient Problem -- 4.6 Some Problems of Detection of Defects -- 4.7 Open Problems -- Chapter 5 Elliptic Equations: Many BoundaryMeasurements -- 5.0 The Dirichlet-to-Neumann Map and theCauchy Set -- 5.1 Boundary Reconstruction -- 5.2 Completeness of Products of Solutions of PDE -- 5.3 Uniqueness and Stability in Ω -- 5.4 Recovery of Several Coefficients -- 5.5 The Plane Case -- 5.6 Nonlinear Equations -- 5.7 Transmission Problems -- 5.8 Maxwell's and Elasticity Systems -- 5.9 Open Problems -- Chapter 6 Scattering Problems and Stationary Waves -- 6.0 Direct Scattering -- 6.1 From A to Near Field -- 6.2 The Inverse Source Problem with Many Wave Numbers -- 6.3 Scattering by a Medium.

6.4 Scattering by Obstacles -- 6.5 Open Problems -- Chapter 7 Integral Geometry and Tomography -- 7.1 The Radon Transform and its Inverse -- 7.2 The Energy Integral Methods -- 7.3 Boman's Counterexample -- 7.4 The Transport Equation -- 7.5 Open Problems -- Chapter 8 Hyperbolic Problems -- 8.0 Introduction -- 8.1 The One-Dimensional Case -- 8.2 Single Boundary Measurements -- 8.3 Many Measurements: The Use of Beam Solutions -- 8.4 Many measurements: Methods of BoundaryControl -- 8.5 Recovery of Discontinuity of the Speedof Propagation -- 8.6 Open Problems -- Chapter 9 Inverse Parabolic Problems -- 9.0 Introduction -- 9.1 Final Overdetermination -- 9.2 Lateral Overdetermination: Single Measurements -- 9.3 The Inverse Problem of Option Pricing -- 9.4 Lateral Overdetermination: Many Measurements -- 9.5 Discontinuous Principal Coefficient and Recovery of a Domain -- 9.6 Nonlinear Equations -- 9.7 Interior Sources -- 9.8 Open Problems -- Chapter 10 Some Numerical Methods -- 10.1 Numerics for the Cauchy Problem -- 10.2 Linearization -- 10.3 Relaxation Methods -- 10.4 Layer Stripping -- 10.5 Range Test Algorithms -- 10.6 Discrete Methods -- Appendix. Function Spaces -- References -- Index.

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