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Funktsional'nyi Analiz i ego Prilozheniya, 2016, Volume 50, Issue 2, Pages 61–74
DOI: https://doi.org/10.4213/faa3230 (Mi faa3230) 		 
This article is cited in 2 scientific papers (total in 3 papers)

Cauchy–Gelfand Problem and the Inverse Problem for a First-Order Quasilinear Equation

G. M. Henkin, A. A. Shananina

a Moscow Institute of Physics and Technology
Full-text PDF (226 kB) Citations (3)
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DOI: https://doi.org/10.4213/faa3230
Abstract: Gelfand's problem on the large time asymptotics of the solution of the Cauchy problem for a first-order quasilinear equation with initial conditions of the Riemann type is considered. Exact asymptotics in the Cauchy–Gelfand problem are obtained and the initial data parameters responsible for the localization of shock waves are described on the basis of the vanishing viscosity method with uniform estimates without the a priori monotonicity assumption for the initial data.
Keywords: quasilinear equation, Cauchy problem, asymptotics, vanishing viscosity method, Maxwell's rule.
Funding agency Grant number
Russian Science Foundation 16-11-10246
This work was supported by the Russian Science Foundation under grant 16-11-10246.
Received: 07.06.2015
English version:
Functional Analysis and Its Applications, 2016, Volume 50, Issue 2, Pages 131–142
DOI: https://doi.org/10.1007/s10688-016-0137-0
Bibliographic databases:
Document Type: Article
UDC: 517.955.8
Language: Russian
Citation: G. M. Henkin, A. A. Shananin, “Cauchy–Gelfand Problem and the Inverse Problem for a First-Order Quasilinear Equation”, Funktsional. Anal. i Prilozhen., 50:2 (2016), 61–74; Funct. Anal. Appl., 50:2 (2016), 131–142
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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