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

TL;DR

This paper studies how to control degenerate singular parabolic equations within finite time using impulse controls, providing explicit decay estimates and establishing the existence and uniqueness of minimal norm controls.

Contribution

It introduces a novel approach combining logarithmic convexity and spectral analysis for finite-time stabilization of degenerate singular parabolic equations.

Findings

Explicit exponential decay estimates for solutions

Existence and uniqueness of minimal norm impulse control

Framework applicable to degenerate singular parabolic systems

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.