Nejib Smaoui, Mona Mekkaoui, "The generalized Burgers equation with and without a time delay", International Journal of Stochastic Analysis, vol. 2004, Article ID 175294, 24 pages, 2004. https://doi.org/10.1155/S1048953304210012
The generalized Burgers equation with and without a time delay
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.
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