The class of evolutionary ferrodynamic equations. (English) Zbl 1473.35533

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

Math. Methods Appl. Sci. 44, No. 15, 11913-11922 (2021).

Summary: The class \(\mathfrak{K}_2\) of evolutionary equations for axial vector fields on \(\mathbb{R}^3\) is described. All operators of the class are invariant with respect to space translations in \(\mathbb{R}^3\), relative to time translations, and they are transformed by covariant way relative to rotations of \(\mathbb{R}^3\). The class \(\mathfrak{M}_2 \subset \mathfrak{K}_2\) of second-order differential operators is studied such that the corresponding evolution equations have the divergent type and each of them preserves the solenoidal property and the unimodality of the field. The explicit form of such operators is found.

MSC:

35Q60	PDEs in connection with optics and electromagnetic theory
35K10	Second-order parabolic equations

Keywords:

axial vector; differential operators; divergence type; Landau-Lifshitz’ equation; solenoidality; unimodality