- 207 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Integral Geometry and Inverse Problems for Kinetic Equations
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
Table of contents
- 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