Carleman estimates and boundary controllability for a class of $ N $ -dimensional degenerate hyperbolic equations

This paper studies the exact boundary controllability of a class of multidimensional weakly degenerate hyperbolic equations with a bounded potential. The degeneracy occurs simultaneously in each coordinate direction. We first establish the well-posedness of the system in weighted Sobolev spaces. A global Carleman estimate is then derived by using a weight function adapted to the degenerate operator. As a consequence, we obtain a hidden regularity result, an observability inequality, and the exact boundary controllability of the system via the Hilbert uniqueness method. The results extend the existing controllability theory for degenerate wave equations from one-dimensional and Grushin-type models to a class of multidimensional coordinate-wise degenerate operators.