  In this letter, a coupled system of viscous Burgers' equations with zero
Dirichlet boundary conditions and appropriate initial data is considered. For
the well-known single viscous Burgers' equation with zero Dirichlet boundary
conditions, the zero equilibrium is the unique global exponential point
attractor. A similar property is shown for the coupled Burgers' equations,
i.e., trajectories starting with initial data which is not too large approach
the zero equilibrium as time goes to infinity. This ``approaching" or
convergence is not necessarily exponentially fast, unlike the single viscous
Burgers' equation.
