Geodesic
A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation
Ignat, Liviu I.1  ; Pozo, Alejandro2, 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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2367-2398

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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.

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DOI : 10.1051/m2an/2017029
Classification : 35B40, 65M12, 35Q35
Keywords: 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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     title = {A semi-discrete large-time behavior preserving scheme for the augmented {Burgers} equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2367--2398},
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     year = {2017},
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     zbl = {1394.65089},
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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

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