A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2367-2398.

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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2017029
Classification : 35B40, 65M12, 35Q35
Mots clés : Augmented Burgers equation, numerical approximation, large-time behavior
Ignat, Liviu I. 1 ; Pozo, Alejandro 2, 3

1 Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania.
2 Asociación Innovalia, Carretera de Asua 6, 48930 Las Arenas - Getxo, Spain.
3 BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain.
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Ignat, Liviu I.; Pozo, Alejandro. A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2367-2398. doi : 10.1051/m2an/2017029. http://www.numdam.org/articles/10.1051/m2an/2017029/

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