This article is cited in 4 papers

Constructing unbounded discontinuous solutions of scalar conservation laws using the Legendre transform

L. V. Gargyants^a, A. Yu. Goritsky^b, E. Yu. Panov<sup>cd

a</sup> Bauman Moscow State Technical University, Moscow, Russia
^b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^c Yaroslav-the-Wise Novgorod State University, Velikii Novgorod, Russia
^d Peoples' Friendship University of Russia, Moscow, Russia

Abstract: A first-order quasilinear equation with an odd flux function that has a single point of inflexion at zero is studied. A method for constructing sign-alternating discontinuous entropy solutions of this equation, based on the Legendre transform, is proposed.
Bibliography: 18 titles.

Keywords: one-dimensional conservation laws, entropy solutions, Legendre transform.

UDC: 517.95

MSC: Primary 35L65; Secondary 35L03

Received: 20.02.2020

DOI: 10.4213/sm9383

 English version: Sbornik: Mathematics, 2021, 212:4, 475–489

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