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This article is cited in 4 scientific papers (total in 4 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
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.
Received: September 21, 2019 Revised: November 19, 2019 Accepted: January 8, 2020
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
Linking options:
https://www.mathnet.ru/eng/tm4066https://doi.org/10.4213/tm4066 https://www.mathnet.ru/eng/tm/v308/p76
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Abstract page: | 396 | Full-text PDF : | 56 | References: | 43 | First page: | 20 |
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