Null Controllability for Degenerate Parabolic Equations with Internal Control Applied on a Measurable Subset

TL;DR

This paper extends previous work by applying a separable variable method to establish null controllability for a different class of degenerate parabolic equations with internal control on a measurable subset.

Contribution

It introduces an alternative approach using the separable variable method to prove controllability for new degenerate parabolic equations.

Findings

Established Lebeau-Robbiano spectral inequality for the new equation.

Proved null controllability with internal control on a measurable subset.

Provided an alternative proof technique for degenerate parabolic equations.

Abstract

This work serves as a continuation of our preceding paper [28]. In that study, we presented a separable variable method to derive the Lebeau-Robbiano spectral inequality for a specific degenerate parabolic equation and subsequently employed it to demonstrate the null controllability of said equation when internal control is applied to an open subset. In the current paper, we reapply the separable variable method to attain the Lebeau-Robbiano spectral inequality for a different degenerate parabolic equation, and we substantiate the null controllability of this equation with internal control acting on a measurable subset. This approach may offer an alternative means of proving controllability results for degenerate parabolic equations.