هندسه انتگرالی و مسائل معکوس برای معادلات جنبشی ۲۰۱۴
Integral Geometry and Inverse Problems for Kinetic Equations 2014

1. Introduction

2. 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

8. 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

16. 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

22. 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

27. Appendix A

28. Bibliography