A SEMI-DISCRETE LARGE-TIME BEHAVIOR PRESERVING SCHEME FOR THE AUGMENTED BURGERS EQUATION

In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain L-1-L-p decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term K * u(xx) is the same as u(xx) for large times. Then, we propose a semi-discrete numerical scheme that preserves this asymptotic behavior, by introducing two correcting factors in the discretization of the non-local term. Numerical experiments illustrating the accuracy of the results of the paper are also presented.