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<p>In this paper, we present a complete description of the class of first-order hyperbolic quasilinear equations of divergent type that describe the change in time <i>t</i> ∈ ℝ of vector fields <Emphasis Type="BoldItalic">υ</Emphasis>(<Emphasis Type="BoldItalic">x, t</Emphasis>), <Emphasis Type="BoldItalic">x</Emphasis> ∈ ℝ<sup>3</sup> that are invariant under translations in time <i>t</i> ∈ ℝ and space ℝ<sup>3</sup> and transform covariantly under the action of the rotation group 𝕆<sub>3</sub> of the space ℝ<sup>3</sup>. This class is compared with the class of similar equations that are hyperbolic in the sense of Friedrichs.</p>

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Hyperbolic Quasilinear Covariant First-Order Equations of Divergent Type for Vector Fields on ℝ3

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Yu. P. Virchenko,
  • A. V. Subbotin

摘要

In this paper, we present a complete description of the class of first-order hyperbolic quasilinear equations of divergent type that describe the change in time t ∈ ℝ of vector fields υ(x, t), x ∈ ℝ3 that are invariant under translations in time t ∈ ℝ and space ℝ3 and transform covariantly under the action of the rotation group 𝕆3 of the space ℝ3. This class is compared with the class of similar equations that are hyperbolic in the sense of Friedrichs.