Integral Geometry and Inverse Problems for Kinetic Equations
VSP International Science Publishers (Verlag)
978-90-6764-352-8 (ISBN)
- Titel erscheint in neuer Auflage
- Artikel merken
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.
Anvar Kh. Amirov, Institute of High Temperatures, Russian Academy of Sciences, Moscow, Russia.
Introduction
Solvability of problems of integral geometry
Two-dimensional inverse problem for the transport equation
Three-dimensional inverse problem for the transport equation
Solvability of the problem of integral geometry along geodesics
A planar problem of integral geometry
Certain problems of tomography
Inverse problems for kinetic equations
The problem of integral geometry and an inverse problem for the kinetic equation
Linear kinetic equation
A modification of problem 2.2.1
One-dimensional kinetic equation
Equations of the Boltzmann type
The Vlasov system
Some inverse and direct problems for the kinetic equation
Evolutionary equations
The Cauchy problem for an integro-differential equation
The problems (3.1.1) – (3.1.2) for m = 2k + 1, p = 1 (the case of nonperiodic solutions)
Boundary value problems
The Cauchy problem for an evolutionary equation
Inverse problem for an evolutionary equation
Inverse problems for second order differential equations
Quantum kinetic equation
Ultrahyperbolic equation
On a class of multidimensional inverse problems
Inverse problems with concentrated data
Appendix
Bibliography
| Erscheint lt. Verlag | 20.12.2001 |
|---|---|
| Reihe/Serie | Inverse and Ill-Posed Problems Series |
| Verlagsort | Zeist |
| Sprache | englisch |
| Gewicht | 480 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 90-6764-352-1 / 9067643521 |
| ISBN-13 | 978-90-6764-352-8 / 9789067643528 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
aus dem Bereich
