Approximation of the conductivity coefficient in the heat equation

In this paper, we study the conductivity coefficient determination in the heat equation from observation of the lateral Dirichlet-to-Neumann map. We define a bilinear form function Q_γ associated to the boundary condition and the Dirichlet-to-Neumann map, and prove that the linearized problem d?Q_γ is injective. Based on the idea of complex geometrical optics solutions, we give two approximations to the conductivity coefficient by using the Fourier truncation method and the mollification method. Under the a priori assumption of the conductivity, we estimate the errors between the conductivity coefficient and its approximations by setting a suitable bound of the frequency.