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

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.