Introduction - UT Mathematics.pdfVIP

Global uniqueness for a coefficient inverse problem for the non-stationary transport equation via Carleman estimate Michael V. Klibanov and Sergey E. Pamyatnykh Department of Mathematics and Statistics, The University of North Carolina at Charlotte, Charlotte, NC 28223, U.S.A. E-mails: mklibanv@, spamyatn@mail.ru Abstract A coefficient inverse problem for the non-stationary single-speed transport equation for t ∈
0, T with the lateral boundary data and initial condition at t
0 is considered. Global uniqueness result is obtained via the method of Carleman estimates. Introduction The transport equation is used to model a variety of processes of particle transport, such as neutron diffusion, scattering of light in the atmosphere, propagation of
−rays in scattering media, etc. (see, e.g., the book of Case and Zweifel [6]). Coefficient inverse problems (CIPs) for the transport equation are the problems of determining of the absorption coefficient, angular density of sources or scattering indicatrix. from an extra boundary data. They have a variety of applications in optical tomography, theory of nuclear reactors, etc. (see, e.g., the book of Anikonov, Kovtanyuk and Prokhorov [1] and references therein). This paper addresses the question of the global uniqueness for a CIP for the non-stationary single-speed transport equation with the extra lateral boundary data. Stability, uniqueness and existence results and references to such results for CIPs for the stationary transport equation can be found, e. e.g., in [1] and in the book of Romanov [25]. Uniqueness and existence results for CIPs for the non-stationary transport equation were obtained in the works of Prilepko and Ivankov [22], [23] and [24]. The results of [22] and [23] were obtained for special