Geodesic
The Burgers equation with periodic boundary conditions on an interval
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 470-476 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the asymptotic profile of the solutions of the Burgers equation on a finite interval with a periodic perturbation on the boundary. The equation describes a dissipative medium, and the initial constant profile therefore passes into a wave with a decreasing amplitude. In the low-viscosity case, the asymptotic profile looks like a sawtooth wave (with periodic breaks of the derivative), similar to the known Fay solution on the half-line, but it has some new properties.
Keywords: sawtooth wave, initial–boundary value problem, asymptotic behavior.
Mots-clés : invariant solution 
@article{TMF_2016_188_3_a7,
     author = {A. V. Samokhin},
     title = {The~Burgers equation with periodic boundary conditions on an~interval},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {470--476},
     year = {2016},
     volume = {188},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a7/}
}
TY  - JOUR
AU  - A. V. Samokhin
TI  - The Burgers equation with periodic boundary conditions on an interval
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 470
EP  - 476
VL  - 188
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a7/
LA  - ru
ID  - TMF_2016_188_3_a7
ER  - 
%0 Journal Article
%A A. V. Samokhin
%T The Burgers equation with periodic boundary conditions on an interval
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 470-476
%V 188
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a7/
%G ru
%F TMF_2016_188_3_a7
A. V. Samokhin. The Burgers equation with periodic boundary conditions on an interval. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 470-476. http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a7/

[1] R. D. Fay, J. Acoust. Soc. Amer., 3 (1931), 222–241 | DOI | Zbl

[2] D. F. Parker, Proc. Roy. Soc. London Ser. A, 369 (1980), 409–424 | DOI | MR | Zbl

[3] O. V. Rudenko, UFN, 165:9 (1995), 1011–1035 | DOI | DOI

[4] A. Samokhin, J. Geom. Phys., 8 (2014), 177–184 | DOI | MR

[5] B. Dubrovin, M. Elaeva, Russ. J. Math. Phys., 19:4 (2012), 449–460, arXiv: 1301.7216 | DOI | MR | Zbl

[6] B. Dubrovin, Commun. Math. Phys., 267:1 (2006), 117–139 | DOI | MR | Zbl