Geodesic
The~Burgers equation with periodic boundary conditions on an~interval
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 470-476

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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 
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     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},
     publisher = {mathdoc},
     volume = {188},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a7/}
}
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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/