Integral Geometry and Inverse Problems for Kinetic Equations
eBook - PDF

Integral Geometry and Inverse Problems for Kinetic Equations

  1. 207 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Integral Geometry and Inverse Problems for Kinetic Equations

Book details
Table of contents
Citations

About This Book

In this monograph a method for proving the solvability of integral geometry problems and inverse problems for kinetic equations is presented. The application of this method has led to interesting problems of the Dirichlet type for third order differential equations, the solvability of which appears to depend on the geometry of the domain for which the problem is stated. Another considered subject is the problem of integral geometry on paraboloids, in particular the uniqueness of solutions to the Goursat problem for a differential inequality, which implies new theorems on the uniqueness of solutions to this problem for a class of quasilinear hyperbolic equations. A class of multidimensional inverse problems associated with problems of integral geometry and the inverse problem for the quantum kinetic equations are also included.

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Yes, you can access Integral Geometry and Inverse Problems for Kinetic Equations by Anvar Kh. Amirov in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2014
ISBN
9783110940947
Edition
1
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics

Table of contents

  1. Introduction
  2. Chapter 1. Solvability of problems of integral geometry
  3. 1.1. Two-dimensional inverse problem for the transport equation
  4. 1.2. Three-dimensional inverse problem for the transport equation
  5. 1.3. Solvability of the problem of integral geometry along geodesics
  6. 1.4. A planar problem of integral geometry
  7. 1.5. Certain problems of tomography
  8. Chapter 2. Inverse problems for kinetic equations
  9. 2.1. The problem of integral geometry and an inverse problem for the kinetic equation
  10. 2.2. Linear kinetic equation
  11. 2.3. A modification of Problem 2.2.1
  12. 2.4. One-dimensional kinetic equation
  13. 2.5. Equations of the Boltzmann type
  14. 2.6. The Vlasov system
  15. 2.7. Some inverse and direct problems for the kinetic equation
  16. Chapter 3. Evolutionary equations
  17. 3.1. The Cauchy problem for an integro-differential equation
  18. 3.2. The problems (3.1.1) - (3.1.2) for m = 2k + 1, p = 1 (the case of nonperiodic solutions)
  19. 3.3. Boundary value problems
  20. 3.4. The Cauchy problem for an evolutionary equation
  21. 3.5. Inverse problem for an evolutionary equation
  22. Chapter 4. Inverse problems for second order differential equations
  23. 4.1. Quantum kinetic equation
  24. 4.2. Ultrahyperbolic equation
  25. 4.3. On a class of multidimensional inverse problems
  26. 4.4. Inverse problems with concentrated data
  27. Appendix A
  28. Bibliography