Stability of solutions to the Burgers equation

Abstract

In this paper we study the boundary stabilization of the Burgers equation. We prove that the closed‐loop system is globally H¹‐stable and H³‐stable and well‐posed. Furthermore, we show that the delayed Burgers' equation is exponentially stable if the delay parameter is sufficiently small. We also give an explicit estimate of the delay parameter in term of the viscosity and the initial condition.