Carleman inequality for a linear degenerate parabolic problem

TL;DR

This paper establishes a Carleman inequality for a degenerate parabolic PDE with a dissipative term, using a specially designed weight function that changes sign within the control domain.

Contribution

It introduces a novel Carleman estimate tailored for degenerate parabolic equations with dissipative terms, expanding the analytical tools for such PDEs.

Findings

Proved a new Carleman inequality for degenerate parabolic problems.

Demonstrated the effectiveness of a sign-changing weight function.

Provides a foundation for controllability results in degenerate PDEs.

Abstract

In this work, we prove a Carleman estimate for a parabolic problem which has a dissipative degenerate term. The prove relies on choose a suitable weight function that change of sign inside the control domain.