Null controllability of degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain

The main purpose of this work is to study numerically a null controllability for a class of one-dimensional degenerate/singular parabolic equations, in divergence and nondivergence form. For this, we resolve an inverse source problem reformulated in a least-squares framework, which leads to a non-convex minimization problem of a cost function $J$, that is solved using a Tikhonov regularization. Firstly, we prove the well-posedness of the minimization problem and the direct problem. Secondly we prove the differentiability of the functional $J$, which gives the existence of the gradient of $J$, that is computed using the adjoint state method. Finally, to show the convergence of the descent method, we prove the Lipschitz continuity of the gradient of $J$. Also we present some numerical experiments.