Carleman estimates for degenerate parabolic equations with single interior degeneracy point and applications
Weijia Wu, Yaozhong Hu, Yuanhang Liu, Donghui Yang · Mathematical Control and Related Fields · 2025
We establish Carleman estimates to study the controllability of a class of $ N $-dimensional degenerate parabolic equations with single interior point degeneracy after proving the existence of solutions of the equations by the Galerkin method. We divide our study into two cases based on whether the degenerate point $ x = 0 $ lies within the control region $ \omega_0 $ or not. We achieve null controllability when $ 0\in\omega_0 $ and obtain approximate controllability when $ 0 otin\omega_0 $.