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Integral Geometry and Inverse Problems for Kinetic Equations.

By: Material type: TextTextSeries: Inverse and Ill-Posed Problems SeriesPublisher: Berlin/Boston : De Gruyter, Inc., 2001Copyright date: ©2001Edition: 1st edDescription: 1 online resource (212 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110940947
Subject(s): Genre/Form: Additional physical formats: Print version:: Integral Geometry and Inverse Problems for Kinetic EquationsLOC classification:
  • QA672 -- .A44 2001eb
Online resources:
Contents:
Intro -- Introduction -- Chapter 1. Solvability of problems of integral geometry -- 1.1. Two-dimensional inverse problem for the transport equation -- 1.2. Three-dimensional inverse problem for the transport equation -- 1.3. Solvability of the problem of integral geometry along geodesics -- 1.4. A planar problem of integral geometry -- 1.5. Certain problems of tomography -- Chapter 2. Inverse problems for kinetic equations -- 2.1. The problem of integral geometry and an inverse problem for the kinetic equation -- 2.2. Linear kinetic equation -- 2.3. A modification of Problem 2.2.1 -- 2.4. One-dimensional kinetic equation -- 2.5. Equations of the Boltzmann type -- 2.6. The Vlasov system -- 2.7. Some inverse and direct problems for the kinetic equation -- Chapter 3. Evolutionary equations -- 3.1. The Cauchy problem for an integro-differential equation -- 3.2. The problems (3.1.1) - (3.1.2) for m = 2k + 1, p = 1 (the case of nonperiodic solutions) -- 3.3. Boundary value problems -- 3.4. The Cauchy problem for an evolutionary equation -- 3.5. Inverse problem for an evolutionary equation -- Chapter 4. Inverse problems for second order differential equations -- 4.1. Quantum kinetic equation -- 4.2. Ultrahyperbolic equation -- 4.3. On a class of multidimensional inverse problems -- 4.4. Inverse problems with concentrated data -- Appendix A -- 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.
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Intro -- Introduction -- Chapter 1. Solvability of problems of integral geometry -- 1.1. Two-dimensional inverse problem for the transport equation -- 1.2. Three-dimensional inverse problem for the transport equation -- 1.3. Solvability of the problem of integral geometry along geodesics -- 1.4. A planar problem of integral geometry -- 1.5. Certain problems of tomography -- Chapter 2. Inverse problems for kinetic equations -- 2.1. The problem of integral geometry and an inverse problem for the kinetic equation -- 2.2. Linear kinetic equation -- 2.3. A modification of Problem 2.2.1 -- 2.4. One-dimensional kinetic equation -- 2.5. Equations of the Boltzmann type -- 2.6. The Vlasov system -- 2.7. Some inverse and direct problems for the kinetic equation -- Chapter 3. Evolutionary equations -- 3.1. The Cauchy problem for an integro-differential equation -- 3.2. The problems (3.1.1) - (3.1.2) for m = 2k + 1, p = 1 (the case of nonperiodic solutions) -- 3.3. Boundary value problems -- 3.4. The Cauchy problem for an evolutionary equation -- 3.5. Inverse problem for an evolutionary equation -- Chapter 4. Inverse problems for second order differential equations -- 4.1. Quantum kinetic equation -- 4.2. Ultrahyperbolic equation -- 4.3. On a class of multidimensional inverse problems -- 4.4. Inverse problems with concentrated data -- Appendix A -- Bibliography.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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