Duan, J. and Nee, J.
Limit Set of Trajectories of the Coupled Viscous Burgers' Equations
(126K, PostScript File)
ABSTRACT. 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.