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Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 2, Pages 61–74 (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

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.


DOI: https://doi.org/10.4213/faa3230

Full text: PDF file (226 kB)
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English version:
Functional Analysis and Its Applications, 2016, 50:2, 131–142

Bibliographic databases:

UDC: 517.955.8
Received: 07.06.2015

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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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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