Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations

TL;DR

This paper develops Carleman estimates and observability inequalities to establish null controllability for interior degenerate non-smooth parabolic equations, advancing control theory in complex PDE settings.

Contribution

It introduces new Carleman estimates and controllability results for parabolic equations with interior degeneracy and non-smooth coefficients, which were not previously addressed.

Findings

Established Carleman estimates for degenerate interior points

Proved observability inequalities for non-smooth coefficients

Achieved null controllability results under new conditions

Abstract

We show Carleman estimates, observability inequalities and null controllability results for parabolic equations with non smooth coefficients degenerating at an interior point.