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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 493, Pages 26–31
DOI: https://doi.org/10.31857/S2686954320040141 (Mi danma90) 		 
This article is cited in 7 scientific papers (total in 7 papers)

MATHEMATICS

On the motion, amplification, and blow-up of fronts in Burgers-type equations with quadratic and modular nonlinearity

N. N. Nefedova, O. V. Rudenkoabc

a Lomonosov Moscow State University, Moscow, Russian Federation
b Prokhorov General Physics Institute of the Russian Academy of Sciences, Moscow, Russian Federation
c Institute of Physics of the Earth, Russian Academy of Scienses, Moscow, Russian Federation
Full-text PDF (189 kB) Citations (7)
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DOI: https://doi.org/10.31857/S2686954320040141
Abstract: A singularly perturbed initial-boundary value problem for a parabolic equation, which is called in applications an equation of Burgers type, is considered. Existence conditions are obtained, and an asymptotic approximation of a new class of solutions with a moving front is constructed. The results are applied to problems with quadratic and modular nonlinearity and nonlinear amplification. The influence of nonlinear amplification on the propagation and destruction of fronts is revealed. Estimates for the blow-up localization and blow-up time are obtained.
Keywords: singularly perturbed parabolic problems, equations of Burgers type, reaction–diffusion–advection equations, internal layers, fronts, asymptotic, methods, blow-up of solutions.
Funding agency Grant number
Russian Science Foundation 18–11–00042
This work was supported by the Russian Science Foundation, project no. 18-11-00042.
Received: 26.05.2020
Revised: 08.06.2020
Accepted: 09.06.2020
English version:
Doklady Mathematics, 2020, Volume 102, Issue 1, Pages 283–287
DOI: https://doi.org/10.1134/S1064562420040146
Bibliographic databases:
Document Type: Article
UDC: 534.222
Language: Russian
Citation: N. N. Nefedov, O. V. Rudenko, “On the motion, amplification, and blow-up of fronts in Burgers-type equations with quadratic and modular nonlinearity”, Dokl. RAN. Math. Inf. Proc. Upr., 493 (2020), 26–31; Dokl. Math., 102:1 (2020), 283–287
Citation in format AMSBIB
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\paper On the motion, amplification, and blow-up of fronts in Burgers-type equations with quadratic and modular nonlinearity
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\pages 26--31
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\transl
\jour Dokl. Math.
\yr 2020
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\pages 283--287
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