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

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. © 2021 Russian Academy of Sciences (DoM) and London Mathematical Society.

Authors
Gargyants L.V. 1 , Goritsky A.Yu. 2 , Panov E.Yu. 3, 4
Journal
Sbornik Mathematics
Publisher
Russian Academy of Sciences
Issue number
4
Language
English
Pages
475-489
State
Published
Link
External link
DOI
10.1070/SM9383
Volume
212
Year
2021
Organizations
  • 1 Bauman Moscow State Technical University, Moscow, Russian Federation
  • 2 Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russian Federation
  • 3 Yaroslav-the-Wise Novgorod State University, Novgorod, Velikii, Russian Federation
  • 4 Peoples' Friendship University of Russia, Moscow, Russian Federation
Keywords
entropy solutions; Legendre transform; one-dimensional conservation laws
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