# Well-posedness and exponential decay estimates for a Korteweg-de Vries-Burgers equation with time-delay

## TL;DR

This paper investigates the well-posedness and exponential decay of solutions for a delayed Korteweg-de Vries-Burgers equation, employing Lyapunov functionals and semigroup theory to establish stability under certain damping conditions.

## Contribution

It introduces a novel analysis of the delayed KdV-Burgers equation, proving well-posedness and decay estimates using a combined Lyapunov and semigroup approach.

## Key findings

- Proved well-posedness of the delayed KdV-Burgers model.
- Established exponential decay under specific damping conditions.
- Applied Lyapunov functionals and semigroup theory for stability analysis.

## Abstract

We consider the KdV-Burgers equation and its linear version in presence of a delay feedback. We prove well-posedness of the models and exponential decay estimates under appropriate conditions on the damping coefficients. Our arguments rely on a Lyapunov functional approach combined with a step by step procedure and semigroup theory.