Abstract

In this talk, we will show our recent results on inverse problems for diffusion equations with discontinuous diffusion coefficients. First, we consider reconstructing the discontinuity of diffusion coefficient from boundary measurements. Two sampling-type methods are established to numerically reconstruct the geometric information on the interface of the medium. Second, we consider an inverse problem of simultaneously recovering the initial value and source strength. A conditional stability is proved, and a numerical algorithm is proposed. Finally, we discuss an inverse problem of simultaneously recovering the initial value and diffusion coefficient. We derive a conditional stability and propose a novel algorithm.