This article is cited in 7 papers

Singularities of Multivalued Solutions of Quasilinear Hyperbolic Systems

I. A. Bogaevsky^ab, D. V. Tunitsky<sup>c

a</sup> Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
^b Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Nakhimovskii pr. 36, korp. 1, Moscow, 117218 Russia
^c V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997 Russia

Abstract: We study the singularities of multivalued solutions of a quasilinear hyperbolic system with two independent and two dependent variables that satisfies the strong nonlinearity condition. For such solutions we obtain a local left–right classification of their projections onto the plane of independent variables at points of finite multiplicity of rank $1$.

Keywords: quasilinear hyperbolic system, multivalued solution, gradient catastrophe, strong nonlinearity condition, singularity of a projection, germ of finite multiplicity, left–right classification.

UDC: 517.956.35+515.164.15+514.763.8

Received: September 21, 2019
Revised: November 19, 2019
Accepted: January 8, 2020

DOI: 10.4213/tm4066

 English version: Proceedings of the Steklov Institute of Mathematics, 2020, 308, 67–78

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