Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation

We consider the inverse problem of identification degenerate diffusion coefficient form $x^\alpha a(x)$ in a one dimensional parabolic equation by some extra data. first prove energy methods uniqueness and Lipschitz stability results for constant $a$ power $\alpha$ knowing an interior data at time. On other hand, we obtain result general coefficients $a(x)$ also boundary on side space interval. The proof is based global Carleman estimates hyperbolic inversion integral transform similar to Laplace transform. Finally, theoretical are satisfactory verified numerically experiments.