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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 308, Pages 76–87
DOI: https://doi.org/10.4213/tm4066 (Mi tm4066) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Singularities of Multivalued Solutions of Quasilinear Hyperbolic Systems

I. A. Bogaevskyab, D. V. Tunitskyc

a 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
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DOI: https://doi.org/10.4213/tm4066
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.
Funding agency Grant number
Russian Foundation for Basic Research 19-51-50005 ЯФ_а
20-01-00610 а
This work was supported by the Russian Foundation for Basic Research and the Japan Society for the Promotion of Science, project no. 19-51-50005. The work of the second author was also supported by the Russian Foundation for Basic Research, project no. 20-01-00610 A.
Received: September 21, 2019
Revised: November 19, 2019
Accepted: January 8, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 308, Pages 67–78
DOI: https://doi.org/10.1134/S008154382001006X
Bibliographic databases:
Document Type: Article
UDC: 517.956.35+515.164.15+514.763.8
Language: Russian
Citation: I. A. Bogaevsky, D. V. Tunitsky, “Singularities of Multivalued Solutions of Quasilinear Hyperbolic Systems”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 308, Steklov Math. Inst. RAS, Moscow, 2020, 76–87; Proc. Steklov Inst. Math., 308 (2020), 67–78
Citation in format AMSBIB
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\pages 76--87
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    • This publication is cited in the following 6 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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