This article is cited in 5 papers

Friedrichs systems for the three-dimensional wave equation

V. M. Gordienko<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk

Abstract: The three-dimensional wave equation is reduced to a Friedrichs symmetric hyperbolic system. We describe all these reductions and find those of them that preserve the velocity of propagation of perturbations. We also exhibit transformations of a Friedrichs system under the Lorentz transformation of coordinates. The construction of the reduction of the wave equation and justification of the properties of this reduction are based on the use of quaternions.

Keywords: wave equation, Friedrichs hyperbolic system, quaternion.

UDC: 517.956.32

Received: 09.09.2009

 English version: Siberian Mathematical Journal, 2010, 51:6, 1013–1027

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