Uniqueness and stabilized algorithm for an inverse problem of identifying space-time dependent diffusion coefficients

In this paper we investigate an inverse problem of identifying the space-time dependent coefficients for diffusion equations with Neumann boundary conditions. The additional data and priori positivity information are preset to uniquely identify the space-time dependent diffusion coefficients. In order to overcome its instability and complexity of space-time function inversion, the inverse problem of diffusion coefficient identification is transformed into an optimization problem with regularized functional. A priori selection strategy of regularization parameter is presented and the convergence rate of the regularized solution is derived. Numerical examples show that the proposed algorithm is effective and applicable to the high-dimensional cases