HYPERBOLIC SPHERICALLY SYMMETRIC FIRST ORDER EQUATION OF DIVERGENT TYPE FOR A VECTOR FIELD

Author(s):  Yu.P. Virchenko, Belgorod National Research University, Belgorod, Russia, virch@bsu.edu.ru

A.A. Pleskanev, candidate of Sciences, associate Professor, Belgorod State Technological University named after V.G. Shukhov, Belgorod , Russia

Issue:  Volume 51, № 2

Rubric:  Physics. Mathematical modeling

Annotation:  It is described the class of evolutionary equations of the first order of divergent type for a vector field a(x, t), x ∈R^3, t∈R, which are invariant relative to time t∈R and spatial translations and which are covariant relative to all group O_3 transformations. Each equation of this class is fully characterized by a pair of differentiable functions f and g which are defined on R^+. In the class of equations found, the class of hyperbolic Friedrichs equations is distinguished. Each equation that is characterized by a pair of functions f and g belongs to this class if and only if the f’g > 0 takes place.

Keywords:  quasilinear systems, hyperbolicity, vector field, covariance, field flux density, symmetric tensors

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