Integral geometry and inverse problems for kinetic equations.

*(English)*Zbl 1040.53001
Inverse and Ill-Posed Problems Series. Utrecht: VSP (ISBN 90-6764-352-1/hbk). vi, 201 p. (2001).

Publisher’s description: In this monograph a new 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 subject of the book 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. This monograph will be of value and interest to mathematicians who deal with problems of integral geometry, direct and inverse problems of mathematical physics and geophysics and for specialists in computerized tomography.

Reviewer: Staniov Grosio (Sofia)

##### MSC:

53-02 | Research exposition (monographs, survey articles) pertaining to differential geometry |

53C65 | Integral geometry |

35R30 | Inverse problems for PDEs |

35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |

35Q72 | Other PDE from mechanics (MSC2000) |

82C40 | Kinetic theory of gases in time-dependent statistical mechanics |

45K05 | Integro-partial differential equations |

45Q05 | Inverse problems for integral equations |

86A22 | Inverse problems in geophysics |

92C55 | Biomedical imaging and signal processing |