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This paper investigates the controllability of a class of $N$-dimensionaldegenerate parabolic equations with interior single-point degeneracy. We employthe Galerkin method to prove the existence of solutions for the equations. Theanalysis is then divided into two cases based on whether the degenerate point$x=0$ lies within the control region $\omega_0$ or not. For each case, weestablish specific Carleman estimates. As a result, we achieve nullcontrollability in the first case $0\in\omega_0$ and unique continuation andapproximate controllability in the second case $0\notin\omega_0$.

Some controllability results of a class of N-dimensional parabolic equations with internal single-point degeneracy