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 con- trollability for a class of one-dimensional degenerate/singular parabolic equa- tions, 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 minimiza- tion 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 com- puted 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.