Abstract
An inverse problem to determine an unknown velocity in two-dimensional, time-independent advection-diffusion equation from data observed at a depth-level is discussed, motivated by an ocean circulation inverse problem. A procedure by which the velocity is reconstructed from the observed data is established and, as a consequence, the uniqueness of the velocity realizing the prescribed data is proved. The procedure involves a modification of the Marchenko method in the inverse scattering theory, based on the Wiener-Hopf factorization and the Riesz-Schauder theory.
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