Friedrichs systems equivalent to the systems of wave equations

Abstract

Description up to equivalence transformations is given for all evolutionary symmetric t-hyperbolic Friedrichs systems equivalent to the systems of two- and three-dimensional wave equations. We obtain the evolutionary symmetric t-hyperbolic Friedrichs systems that describe shear waves in a three-dimensional isotropic elastic medium both in the presence and absence of mass forces. Studying the group properties of some of these systems, we point out a system equivalent to the Maxwell equations for the electromagnetic field in vacuum that consists of the equations in involution under charge conservation of an evolutionary symmetric t-hyperbolic Friedrichs system and the Lorentz condition.