Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Copyright © 2004 Nejib Smaoui and Mona Mekkaoui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the generalized Burgers equation with and without a
time delay when the boundary conditions are
periodic with period . For the generalized Burgers equation
without a time delay, that is, , , , , , a Lyapunov function method is used to show boundedness and uniqueness of a steady state solution and global stability of the
equation. As for the generalized time-delayed Burgers equation,
that is, , , , , , , , , we show
that the equation is exponentially stable under small
delays. Using a pseudospectral method, we present some numerical
results illustrating and reinforcing the analytical results.