Geodesic
Description of a class of evolutionary equations in ferrodynamics
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 1, Tome 170 (2019), pp. 15-30

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In this paper, we state the problem of constructing evolution equations describing the dynamics of condensed matter with an internal structure. Within the framework of this statement, we describe the class of evolution equations for vector and pseudovector fields on $\mathbb{R}^3$ with an infinitesimal shift defined by a second-order, divergent-type differential operator, which is invariant under translations of $\mathbb{R}^3$ and time translations and is transformed covariantly under rotations of $\mathbb{R}^3$. The case of equations of this class with preserved solenoidality and unimodality of the field is studied separately. A general formula for all operators corresponding to these equations is established.
Keywords: divergent differential operator, pseudovector field, flux density, unimodality, solenoidality, ferrodynamic equation. 
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     author = {Yu. P. Virchenko and A. V. Subbotin},
     title = {Description of a class of evolutionary equations in ferrodynamics},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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Yu. P. Virchenko; A. V. Subbotin. Description of a class of evolutionary equations in ferrodynamics. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 1, Tome 170 (2019), pp. 15-30. http://geodesic.mathdoc.fr/item/INTO_2019_170_a1/