Identification of the diffusion coefficient in a one-dimensional parabolic equation

This paper deals with the problem of the identification of the diffusion coefficient in a parabolic equation. This inverse problem is formulated as a nonlinear operator equation in Hilbert spaces. Continuity and differentiability of the corresponding operator is shown. In the one-dimensional case uniqueness and conditional stability results are obtained by using the heat equation transform. Finally, the problem is solved numerically by iteratively regularized Gauss-Newton method.