A note on Burgers' equation with time delay: Instability via finite-time blow-up

Burgers' equation with time delay is considered. Using the Cole-Hopf transformation, the exact solution of this nonlinear partial differential equation (PDE) is determined in the context of a (seemingly) well-posed initial-boundary value problem (IBVP) involving homogeneous Dirichlet data. The solution obtained, however, is shown to exhibit a delay-induced instability, suffering blow-up in finite-time.