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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 188, Number 3, Pages 470–476
DOI: https://doi.org/10.4213/tmf9075 (Mi tmf9075) 		 
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
Full-text PDF (451 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf9075
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.
English version:
Theoretical and Mathematical Physics, 2016, Volume 188, Issue 3, Pages 1371–1376
DOI: https://doi.org/10.1134/S0040577916090087
Bibliographic databases:
PACS: 43.25.+y
MSC: 35Q35, 35Q53
Language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9075
  • https://doi.org/10.4213/tmf9075
  • https://www.mathnet.ru/eng/tmf/v188/i3/p470
    • This publication is cited in the following 2 articles:
    1. Pintu Samanta, Ch. Srinivasa Rao, “Asymptotic Solutions of Burgers Equation and Modified Burgers Equation Satisfying Flux Type Conditions”, Int. J. Appl. Comput. Math, 8:4 (2022)  crossref
    2. A. Samokhin, “On nonlinear superposition of the KdV-Burgers shock waves and the behavior of solitons in a layered medium”, Differ. Geom. Appl., 54:A (2017), 91–99  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:445
    Full-text PDF :236
    References:63
    First page:35
     
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