# Null controllability of a degenerate parabolic equation with delay

## TL;DR

This paper investigates the null controllability of a linear degenerate parabolic equation with delay, using Carleman estimates to establish controllability results and exploring boundary control issues.

## Contribution

It introduces novel controllability results for degenerate parabolic equations with delay using Carleman estimates and discusses boundary control problems.

## Key findings

- Carleman estimates effectively establish null controllability.
- Boundary control problems are addressed for degenerate parabolic equations with delay.
- New techniques for controlling delayed degenerate PDEs are proposed.

## Abstract

We are concerned about the null controllability of a linear degenerate parabolic equation with one delay parameter on the line $(0,1)$, where the control force is exerted on a subdomain of $(0,1)$ or on the boundary. For that we show how Carleman estimate can be used to establish such results. The second novelty, we discus the problem of boundary control for parabolic degenerate equations with delay.