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This article is cited in 2 scientific papers (total in 2 papers)
The Burgers equation with periodic boundary conditions on an interval
A. V. Samokhin Moscow State Technical University of Civil Aviation, Moscow,
Russia
Abstract:
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, invariant solution, initial–boundary value problem,
asymptotic behavior.
Citation:
A. V. Samokhin, “The Burgers equation with periodic boundary conditions on an interval”, TMF, 188:3 (2016), 470–476; Theoret. and Math. Phys., 188:3 (2016), 1371–1376
Linking options:
https://www.mathnet.ru/eng/tmf9075https://doi.org/10.4213/tmf9075 https://www.mathnet.ru/eng/tmf/v188/i3/p470
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Abstract page: | 409 | Full-text PDF : | 212 | References: | 52 | First page: | 35 |
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