| Issue |
Math. Model. Nat. Phenom.
Volume 14, Number 4, 2019
Singular perturbations and multiscale systems
|
|
|---|---|---|
| Article Number | 401 | |
| Number of page(s) | 14 | |
| DOI | https://doi.org/10.1051/mmnp/2019009 | |
| Published online | 02 April 2019 | |
The existence and asymptotic stability of periodic solutions with an interior layer of Burgers type equations with modular advection★
Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University,
19899
Moscow, Russia.
* Corresponding author: nefedov@phys.msu.ru
Received:
25
October
2018
Accepted:
30
January
2019
We consider a new class of singularly perturbed parabolic periodic boundary value problems for reaction-advection-diffusion equations: Burgers type equations with modular advection. We construct the interior layer type formal asymptotics and propose a modified procedure to get asymptotic lower and upper solutions. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution with an interior layer and estimate the accuracy of its asymptotics. The asymptotic stability of this solution is also established.
Mathematics Subject Classification: 35L05 / 35L70
Key words: Singularly perturbed parabolic periodic problems / Burgers type equations / exponential asymptotic stability / lower and upper solutions
© EDP Sciences, 2019
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