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Inverse problem for a kinetic equation

/. Inv. -Posed Problems, Vol.3, No.5, pp.351-357 (1995) © VSP 1995 . AMIRO V* Received October 9, 1994 Abstract -- We consider a problem of simultaneous by determining the solution and the right-hand side of a kinetic equation provided that the solution is given at the domain boundary. We prove that the solution exists and is unique if certain quadratic forms connected with the equation are positive or negative definite. 1. We examine the inverse problem for a kinetic equation. The author's strongest reason for this investigation is that it is connected with a problem of integral geometry. Besides, inverse problems for kinetic equations are theoretically and practically important in tomography, seismology, plasma physics etc. Physically, these inverse problems are to determine interaction forces, absorptivities, sources, scattering indicatrices (radar crosssections) and other quantities. Interesting results concerning the inverse problems for kinetic equations have been obtained in [2,3,6]. The previous works in this field were mainly devoted to problems of determining isotropic sources. We consider here an inverse problem for a kinetic equation in which the source substantially depends on the velocity (see also [2,3] for the solution uniqueness). This allows us to extend the class of solution uniqueness http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and Ill-Posed Problems de Gruyter

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