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(gamma) associated to the boundary condition and the Dirichlet-to-Neumann map, and prove that the linearized problem d Q(gamma) 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.