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Cauchy–Gelfand problem and the inverse problem for a first-order quasilinear equation

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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.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia

    G. M. Khenkin & A. A. Shananin

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  1. G. M. Khenkin
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  2. A. A. Shananin
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Correspondence to A. A. Shananin.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 50, No. 2, pp. 61–74, 2016

Original Russian Text Copyright © by G. M. Khenkin † and A. A. Shananin

This work was supported by the Russian Science Foundation under grant 16-11-10246.

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Khenkin, G.M., Shananin, A.A. Cauchy–Gelfand problem and the inverse problem for a first-order quasilinear equation. Funct Anal Its Appl 50, 131–142 (2016). https://doi.org/10.1007/s10688-016-0137-0

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  • DOI: https://doi.org/10.1007/s10688-016-0137-0

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