Finite-time stabilization via impulse control of degenerate singular parabolic equations

Abstract

This paper examines the impulse controllability of degenerate singular parabolic equations through a modern framework focused on finite-time stabilization. Furthermore, we provide an explicit estimate for the exponential decay of the solution. The proof of our main result combines a logarithmic convexity estimate with specific spectral properties. Finally, we establish the existence and uniqueness of the minimal norm impulse control associated with the system.