This article is cited in 2 papers

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

G. M. Henkin, A. A. Shananin<sup>a

a</sup> 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.

UDC: 517.955.8

Received: 07.06.2015

DOI: 10.4213/faa3230

 English version: Functional Analysis and Its Applications, 2016, 50:2, 131–142

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