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 L1-Lp decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term K ∗ uxx is the same as u...
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| Veröffentlicht in: | ESAIM. Mathematical modelling and numerical analysis 2017-11, Vol.51 (6), p.2367-2398 |
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| creator | Ignat, Liviu I. Pozo, Alejandro |
| description | 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 L1-Lp decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term K ∗ uxx is the same as uxx 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. |
| doi_str_mv | 10.1051/m2an/2017029 |
| format | Article |
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| language | eng |
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| source | Alma/SFX Local Collection |
| subjects | 35B40 35Q35 65M12 Asymptotic properties Augmented Burgers equation Burgers equation Cauchy problems Convolution Decay rate Economic models large-time behavior Linear equations numerical approximation Well posed problems |
| title | A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation |
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