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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