Geodesic
Hyperbolicity of a class of first-order quasilinear covariant equations of divergent type
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 16-26

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A special class of systems of first-order quasilinear partial differential equations is considered. These divergent-type systems are invariant under time and space translations; they are transformed covariantly under the action of the rotation group. We give a description of the class of nonlinear first-order differential operators corresponding to the systems of the considered class and prove a theorem on the equivalence of the concepts of hyperbolicity and hyperbolicity in the sense of Friedrichs.
Keywords: first-order differential operator, quasilinear system, hyperbolicity, vector field, covariance, field flux density, symmetric tensor.
Mots-clés : divergence 
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     author = {Yu. P. Virchenko and A. E. Novoseltseva},
     title = {Hyperbolicity of a class of first-order quasilinear covariant equations of divergent type},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {16--26},
     publisher = {mathdoc},
     volume = {207},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_207_a2/}
}
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Yu. P. Virchenko; A. E. Novoseltseva. Hyperbolicity of a class of first-order quasilinear covariant equations of divergent type. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 16-26. http://geodesic.mathdoc.fr/item/INTO_2022_207_a2/