Friedrichs systems equivalent to the systems of wave equations

Yu. A. Chirkunov

Novosibirsk State Technical University, Novosibirsk, RUSSIA

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.

Keywords: Friedrichs system, wave equations, equivalence transformation, equivalent systems, shear wave in a three-dimensional isotropic elastic medium, Maxwell's equations, involution.

UDC: 517.9+539.3

Received: 16.04.2009

 English version: Journal of Applied and Industrial Mathematics, 2012, 6:2, 150–159

Bibliographic databases:

•