Abstract

This paper is devoted to study of complex geometrical optics (CGO) solutions to the coupled conductivity equations written in a matrix form div (Q center dot del U) - 0 in R-2 for symmetric, positive definite matrix functions Q. The CGO solutions were introduced by Faddeev in 1966 [8] to prove the uniqueness in the inverse potential scattering problem for Schodinger equation, later Sylvester and Uhlmann in 1987 [26] use the CGO functions to study the uniqueness of the Calderon's inverse problem. Following the ideas of Astala and Paivarinta [3], we compute CGO solutions considering the vectorial solutions of an associated Beltrami system. In this work, we first prove the existence of CGO solution and then use a numerical strategy based on the method introduced by Huhtanem and Peramaki in [12] for the Beltrami equation. Numerical experiments are considered to show the influence of coupled equations.