Determination of Two Convection Coefficients from Dirichlet to Neumann Map in the Two-Dimensional Case

In the two-dimensional case, we consider the problem of determining two convection coefficients from the Dirichlet to Neumann map. With the theory of generalized analytic functions which was developed by Bers and Vekua, we can formulate the problem as an inverse problem for a first order elliptic system. By using the inverse scattering method for the first order elliptic system, we prove that, in two dimensions, the Dirichlet to Neumann map uniquely determines two convection coefficients without any smallness assumption of unknown coefficients.