The purpose of this article is to define the radiation fields on asymptotically hyperbolic manifolds and to use them to study scattering theory. The radiation fields on R n and on asymptotically Euclidean manifolds were introduced by F.G. Friedlander in a series of papers starting in the early 1960’s [10, 11, 12, 13, 14]. His program of using the radiation fields to obtain the scattering matrix in that general setting was

Abstract. We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval [0, T] so that all signals issued from the domain leave it after time T. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give almost necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary. 1.

: We consider the problem of recovering the coefficient q(x) in the equation u t = \Delta\Delta \Deltau \Gamma qu from boundary observations. Uniqueness of q based on knowledge of the `Neumann 7! Dirichlet response operator' is shown as an implication of (known) corresponding results concerning the inverse problem for the corresponding hyperbolic equation w tt = \Delta\Delta \Delta w \Gamma qw. This is then reduced to use of the response to a single input with some consideration of computational approximation. Key Words: identification, parabolic, partial differential equation, uniqueness, approximation. 1 This research has been partially supported by the U.S. National Academy of Science under the NAS/NRC Project Development Program. 1. Introduction We consider the problem of identifying the (unknown) coefficient q = q(x) in the parabolic partial differential equation u t = \Delta\Delta \Deltau \Gamma qu on Q := (0; T ) \Theta\Omega ; (1.1) assuming input/output access only a...