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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 196, Number 1, Pages 42–49
DOI: https://doi.org/10.4213/tmf9479 (Mi tmf9479) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Asymptotic solution of the multidimensional Burgers equation near a singularity

S. V. Zakharov

Krasovskii Institute for Mathematics and Mechanics, Ural Branch, RAS, Ekaterinenburg, Russia
Full-text PDF (460 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf9479
Abstract: We consider the Cauchy problem for the multidimensional Burgers equation with a small dissipation parameter and use the matching method to construct an asymptotic solution near the singularity determined by the vector field structure at the initial instant. The method that we use allows tracing the evolution of the solution with a hierarchy of differently scaled structures and giving a rigorous mathematical definition of the asymptotic solution in the leading approximation. We discuss the relation of the considered problem to different models in fundamental and applied physics.
Keywords: multidimensional Burgers equation, Cauchy problem, asymptotics.
Funding agency Grant number
Ural Branch of the Russian Academy of Sciences 0387-2016-0039
This research is supported by the complex Program for Basic Research, Ural Branch, RAS, “Analytic, asymptotic, and numerical methods for constructing direct, inverse, and singularly perturbed problems of mathematical physics” (Project No. 0387-2016-0039).
Received: 09.10.2017
Revised: 23.01.2018
English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 1, Pages 976–982
DOI: https://doi.org/10.1134/S0040577918070048
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. V. Zakharov, “Asymptotic solution of the multidimensional Burgers equation near a singularity”, TMF, 196:1 (2018), 42–49; Theoret. and Math. Phys., 196:1 (2018), 976–982
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9479
  • https://www.mathnet.ru/eng/tmf/v196/i1/p42
    • This publication is cited in the following 5 articles:
    1. S. V. Zakharov, “Constructing the asymptotics of a solution of the heat equation from the known asymptotics of the initial function in three-dimensional space”, Sb. Math., 215:1 (2024), 101–118  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. S. V. Zakharov, “Reconstructions of the asymptotics of an integral determined by a hyperbolic unimodal singularity”, Funct. Anal. Appl., 57:4 (2023), 314–325  mathnet  crossref  crossref
    3. Sergey V. Zakharov, “Evolution of a multiscale singularity of the solution of the Burgers equation in the 4-dimensional space-time”, Ural Math. J., 8:1 (2022), 136–144  mathnet  crossref  mathscinet
    4. S. V. Zakharov, “Singular points and asymptotics in the singular Cauchy problem for the parabolic equation with a small parameter”, Comput. Math. Math. Phys., 60:5 (2020), 821–832  mathnet  mathnet  crossref  crossref  mathscinet  isi  scopus
    5. Sergey V. Zakharov, “Asymptotic solutions of a parabolic equation near singular points of A and B types”, Ural Math. J., 5:1 (2019), 101–108  mathnet  crossref  mathscinet  zmath
    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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